cats-in-sweaters.sage

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)