A318257 Triangle read by rows, expansion of the e.g.f. given below related to partitions of {1,2,...,5n} into sets of size 5, nonzero coefficients of z.
1, 0, 1, 0, 1, 126, 0, 1, 3003, 126126, 0, 1, 107882, 23279256, 488864376, 0, 1, 3321890, 5319906900, 412275623760, 5194672859376, 0, 1, 107746281, 1394769716340, 369277150181940, 14687937509885640, 123378675083039376
Offset: 0
Examples
[0] [1] [1] [0, 1] [2] [0, 1, 126] [3] [0, 1, 3003, 126126] [4] [0, 1, 107882, 23279256, 488864376] [5] [0, 1, 3321890, 5319906900, 412275623760, 5194672859376]
Programs
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Maple
CL := p -> PolynomialTools:-CoefficientList(p, x): FL := p -> ListTools:-Flatten(p): f := z -> (1/5)*(exp(z)+2*(+exp(1/4*z*(5^(1/2)-1))*cos(1/4*z*2^(1/2)* (5+5^(1/2))^(1/2))+exp(-1/4*z*(5^(1/2)+1))*cos(1/4*z*2^(1/2)*(5-5^(1/2))^(1/2)))): gf := exp(x*(f(z)-1)): ser := series(gf, z, 48): FL([seq(CL(sort(expand((5*n)!*coeff(ser, z, n*5)), [x], ascending)),n=0..7)]);