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

Author

Peter Luschny, Aug 22 2018

Keywords

• nonn
• tabl

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]
		

Crossrefs

Cf. A048993 (m=1), A156289 (m=2), A291451 (m=3), A291452 (m=4), this seq (m=5).

Programs

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)]);