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November 8, 2019 15:04
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sage: var("x, y") | |
....: f = exp(x) / (1 - (1+x)*y) | |
....: | |
....: for (c, i) in f.taylor(x, 0, 13).coefficients(): | |
....: fac = factorial(i) | |
....: for (d, j) in c.taylor(y, 0, 13).coefficients(): | |
....: print(i, j, d * fac) | |
....: | |
(x, y) | |
(0, 0, 1) | |
(0, 1, 1) | |
(0, 2, 1) | |
(0, 3, 1) | |
(0, 4, 1) | |
(0, 5, 1) | |
(0, 6, 1) | |
(0, 7, 1) | |
(0, 8, 1) | |
(0, 9, 1) | |
(0, 10, 1) | |
(0, 11, 1) | |
(0, 12, 1) | |
(0, 13, 1) | |
(1, 0, 1) | |
(1, 1, 2) | |
(1, 2, 3) | |
(1, 3, 4) | |
(1, 4, 5) | |
(1, 5, 6) | |
(1, 6, 7) | |
(1, 7, 8) | |
(1, 8, 9) | |
(1, 9, 10) | |
(1, 10, 11) | |
(1, 11, 12) | |
(1, 12, 13) | |
(1, 13, 14) | |
(2, 0, 1) | |
(2, 1, 3) | |
(2, 2, 7) | |
(2, 3, 13) | |
(2, 4, 21) | |
(2, 5, 31) | |
(2, 6, 43) | |
(2, 7, 57) | |
(2, 8, 73) | |
(2, 9, 91) | |
(2, 10, 111) | |
(2, 11, 133) | |
(2, 12, 157) | |
(2, 13, 183) | |
(3, 0, 1) | |
(3, 1, 4) | |
(3, 2, 13) | |
(3, 3, 34) | |
(3, 4, 73) | |
(3, 5, 136) | |
(3, 6, 229) | |
(3, 7, 358) | |
(3, 8, 529) | |
(3, 9, 748) | |
(3, 10, 1021) | |
(3, 11, 1354) | |
(3, 12, 1753) | |
(3, 13, 2224) | |
(4, 0, 1) | |
(4, 1, 5) | |
(4, 2, 21) | |
(4, 3, 73) | |
(4, 4, 209) | |
(4, 5, 501) | |
(4, 6, 1045) | |
(4, 7, 1961) | |
(4, 8, 3393) | |
(4, 9, 5509) | |
(4, 10, 8501) | |
(4, 11, 12585) | |
(4, 12, 18001) | |
(4, 13, 25013) | |
(5, 0, 1) | |
(5, 1, 6) | |
(5, 2, 31) | |
(5, 3, 136) | |
(5, 4, 501) | |
(5, 5, 1546) | |
(5, 6, 4051) | |
(5, 7, 9276) | |
(5, 8, 19081) | |
(5, 9, 36046) | |
(5, 10, 63591) | |
(5, 11, 106096) | |
(5, 12, 169021) | |
(5, 13, 259026) | |
(6, 0, 1) | |
(6, 1, 7) | |
(6, 2, 43) | |
(6, 3, 229) | |
(6, 4, 1045) | |
(6, 5, 4051) | |
(6, 6, 13327) | |
(6, 7, 37633) | |
(6, 8, 93289) | |
(6, 9, 207775) | |
(6, 10, 424051) | |
(6, 11, 805597) | |
(6, 12, 1442173) | |
(6, 13, 2456299) | |
(7, 0, 1) | |
(7, 1, 8) | |
(7, 2, 57) | |
(7, 3, 358) | |
(7, 4, 1961) | |
(7, 5, 9276) | |
(7, 6, 37633) | |
(7, 7, 130922) | |
(7, 8, 394353) | |
(7, 9, 1047376) | |
(7, 10, 2501801) | |
(7, 11, 5470158) | |
(7, 12, 11109337) | |
(7, 13, 21204548) | |
(8, 0, 1) | |
(8, 1, 9) | |
(8, 2, 73) | |
(8, 3, 529) | |
(8, 4, 3393) | |
(8, 5, 19081) | |
(8, 6, 93289) | |
(8, 7, 394353) | |
(8, 8, 1441729) | |
(8, 9, 4596553) | |
(8, 10, 12975561) | |
(8, 11, 32989969) | |
(8, 12, 76751233) | |
(8, 13, 165625929) | |
(9, 0, 1) | |
(9, 1, 10) | |
(9, 2, 91) | |
(9, 3, 748) | |
(9, 4, 5509) | |
(9, 5, 36046) | |
(9, 6, 207775) | |
(9, 7, 1047376) | |
(9, 8, 4596553) | |
(9, 9, 17572114) | |
(9, 10, 58941091) | |
(9, 11, 175721140) | |
(9, 12, 472630861) | |
(9, 13, 1163391958) | |
(10, 0, 1) | |
(10, 1, 11) | |
(10, 2, 111) | |
(10, 3, 1021) | |
(10, 4, 8501) | |
(10, 5, 63591) | |
(10, 6, 424051) | |
(10, 7, 2501801) | |
(10, 8, 12975561) | |
(10, 9, 58941091) | |
(10, 10, 234662231) | |
(10, 11, 824073141) | |
(10, 12, 2581284541) | |
(10, 13, 7307593151) | |
(11, 0, 1) | |
(11, 1, 12) | |
(11, 2, 133) | |
(11, 3, 1354) | |
(11, 4, 12585) | |
(11, 5, 106096) | |
(11, 6, 805597) | |
(11, 7, 5470158) | |
(11, 8, 32989969) | |
(11, 9, 175721140) | |
(11, 10, 824073141) | |
(11, 11, 3405357682) | |
(11, 12, 12470162233) | |
(11, 13, 40864292184) | |
(12, 0, 1) | |
(12, 1, 13) | |
(12, 2, 157) | |
(12, 3, 1753) | |
(12, 4, 18001) | |
(12, 5, 169021) | |
(12, 6, 1442173) | |
(12, 7, 11109337) | |
(12, 8, 76751233) | |
(12, 9, 472630861) | |
(12, 10, 2581284541) | |
(12, 11, 12470162233) | |
(12, 12, 53334454417) | |
(12, 13, 202976401213) | |
(13, 0, 1) | |
(13, 1, 14) | |
(13, 2, 183) | |
(13, 3, 2224) | |
(13, 4, 25013) | |
(13, 5, 259026) | |
(13, 6, 2456299) | |
(13, 7, 21204548) | |
(13, 8, 165625929) | |
(13, 9, 1163391958) | |
(13, 10, 7307593151) | |
(13, 11, 40864292184) | |
(13, 12, 202976401213) | |
(13, 13, 896324308634) |
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