cats-in-sweaters-and-bows.sage

sage: var("x1, x2, y")
....: f = exp(x1 + x2) / (1 - (1+x1)*(1+x2)*y)
....: 
....: for (c, i) in f.taylor(x1, 0, 5).coefficients():
....:     fac1 = factorial(i)
....:     for (d, j) in c.taylor(x2, 0, 5).coefficients():
....:         fac = fac1 * factorial(j)
....:         for (e, k) in d.taylor(y, 0, 5).coefficients():
....:             print(i, j, k, e * fac)
....: 
(x1, x2, y)
(0, 0, 0, 1)
(0, 0, 1, 1)
(0, 0, 2, 1)
(0, 0, 3, 1)
(0, 0, 4, 1)
(0, 0, 5, 1)
(0, 1, 0, 1)
(0, 1, 1, 2)
(0, 1, 2, 3)
(0, 1, 3, 4)
(0, 1, 4, 5)
(0, 1, 5, 6)
(0, 2, 0, 1)
(0, 2, 1, 3)
(0, 2, 2, 7)
(0, 2, 3, 13)
(0, 2, 4, 21)
(0, 2, 5, 31)
(0, 3, 0, 1)
(0, 3, 1, 4)
(0, 3, 2, 13)
(0, 3, 3, 34)
(0, 3, 4, 73)
(0, 3, 5, 136)
(0, 4, 0, 1)
(0, 4, 1, 5)
(0, 4, 2, 21)
(0, 4, 3, 73)
(0, 4, 4, 209)
(0, 4, 5, 501)
(0, 5, 0, 1)
(0, 5, 1, 6)
(0, 5, 2, 31)
(0, 5, 3, 136)
(0, 5, 4, 501)
(0, 5, 5, 1546)
(1, 0, 0, 1)
(1, 0, 1, 2)
(1, 0, 2, 3)
(1, 0, 3, 4)
(1, 0, 4, 5)
(1, 0, 5, 6)
(1, 1, 0, 1)
(1, 1, 1, 4)
(1, 1, 2, 9)
(1, 1, 3, 16)
(1, 1, 4, 25)
(1, 1, 5, 36)
(1, 2, 0, 1)
(1, 2, 1, 6)
(1, 2, 2, 21)
(1, 2, 3, 52)
(1, 2, 4, 105)
(1, 2, 5, 186)
(1, 3, 0, 1)
(1, 3, 1, 8)
(1, 3, 2, 39)
(1, 3, 3, 136)
(1, 3, 4, 365)
(1, 3, 5, 816)
(1, 4, 0, 1)
(1, 4, 1, 10)
(1, 4, 2, 63)
(1, 4, 3, 292)
(1, 4, 4, 1045)
(1, 4, 5, 3006)
(1, 5, 0, 1)
(1, 5, 1, 12)
(1, 5, 2, 93)
(1, 5, 3, 544)
(1, 5, 4, 2505)
(1, 5, 5, 9276)
(2, 0, 0, 1)
(2, 0, 1, 3)
(2, 0, 2, 7)
(2, 0, 3, 13)
(2, 0, 4, 21)
(2, 0, 5, 31)
(2, 1, 0, 1)
(2, 1, 1, 6)
(2, 1, 2, 21)
(2, 1, 3, 52)
(2, 1, 4, 105)
(2, 1, 5, 186)
(2, 2, 0, 1)
(2, 2, 1, 9)
(2, 2, 2, 49)
(2, 2, 3, 169)
(2, 2, 4, 441)
(2, 2, 5, 961)
(2, 3, 0, 1)
(2, 3, 1, 12)
(2, 3, 2, 91)
(2, 3, 3, 442)
(2, 3, 4, 1533)
(2, 3, 5, 4216)
(2, 4, 0, 1)
(2, 4, 1, 15)
(2, 4, 2, 147)
(2, 4, 3, 949)
(2, 4, 4, 4389)
(2, 4, 5, 15531)
(2, 5, 0, 1)
(2, 5, 1, 18)
(2, 5, 2, 217)
(2, 5, 3, 1768)
(2, 5, 4, 10521)
(2, 5, 5, 47926)
(3, 0, 0, 1)
(3, 0, 1, 4)
(3, 0, 2, 13)
(3, 0, 3, 34)
(3, 0, 4, 73)
(3, 0, 5, 136)
(3, 1, 0, 1)
(3, 1, 1, 8)
(3, 1, 2, 39)
(3, 1, 3, 136)
(3, 1, 4, 365)
(3, 1, 5, 816)
(3, 2, 0, 1)
(3, 2, 1, 12)
(3, 2, 2, 91)
(3, 2, 3, 442)
(3, 2, 4, 1533)
(3, 2, 5, 4216)
(3, 3, 0, 1)
(3, 3, 1, 16)
(3, 3, 2, 169)
(3, 3, 3, 1156)
(3, 3, 4, 5329)
(3, 3, 5, 18496)
(3, 4, 0, 1)
(3, 4, 1, 20)
(3, 4, 2, 273)
(3, 4, 3, 2482)
(3, 4, 4, 15257)
(3, 4, 5, 68136)
(3, 5, 0, 1)
(3, 5, 1, 24)
(3, 5, 2, 403)
(3, 5, 3, 4624)
(3, 5, 4, 36573)
(3, 5, 5, 210256)
(4, 0, 0, 1)
(4, 0, 1, 5)
(4, 0, 2, 21)
(4, 0, 3, 73)
(4, 0, 4, 209)
(4, 0, 5, 501)
(4, 1, 0, 1)
(4, 1, 1, 10)
(4, 1, 2, 63)
(4, 1, 3, 292)
(4, 1, 4, 1045)
(4, 1, 5, 3006)
(4, 2, 0, 1)
(4, 2, 1, 15)
(4, 2, 2, 147)
(4, 2, 3, 949)
(4, 2, 4, 4389)
(4, 2, 5, 15531)
(4, 3, 0, 1)
(4, 3, 1, 20)
(4, 3, 2, 273)
(4, 3, 3, 2482)
(4, 3, 4, 15257)
(4, 3, 5, 68136)
(4, 4, 0, 1)
(4, 4, 1, 25)
(4, 4, 2, 441)
(4, 4, 3, 5329)
(4, 4, 4, 43681)
(4, 4, 5, 251001)
(4, 5, 0, 1)
(4, 5, 1, 30)
(4, 5, 2, 651)
(4, 5, 3, 9928)
(4, 5, 4, 104709)
(4, 5, 5, 774546)
(5, 0, 0, 1)
(5, 0, 1, 6)
(5, 0, 2, 31)
(5, 0, 3, 136)
(5, 0, 4, 501)
(5, 0, 5, 1546)
(5, 1, 0, 1)
(5, 1, 1, 12)
(5, 1, 2, 93)
(5, 1, 3, 544)
(5, 1, 4, 2505)
(5, 1, 5, 9276)
(5, 2, 0, 1)
(5, 2, 1, 18)
(5, 2, 2, 217)
(5, 2, 3, 1768)
(5, 2, 4, 10521)
(5, 2, 5, 47926)
(5, 3, 0, 1)
(5, 3, 1, 24)
(5, 3, 2, 403)
(5, 3, 3, 4624)
(5, 3, 4, 36573)
(5, 3, 5, 210256)
(5, 4, 0, 1)
(5, 4, 1, 30)
(5, 4, 2, 651)
(5, 4, 3, 9928)
(5, 4, 4, 104709)
(5, 4, 5, 774546)
(5, 5, 0, 1)
(5, 5, 1, 36)
(5, 5, 2, 961)
(5, 5, 3, 18496)
(5, 5, 4, 251001)
(5, 5, 5, 2390116)