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

0,6

Links

Table of n, a(n) for n=0..27.

Example

[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]

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)]);

Crossrefs

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

Sequence in context: A048563 A239060 A365898 * A110825 A365897 A050451

Adjacent sequences: A318254 A318255 A318256 * A318258 A318259 A318260

Keyword

nonn,tabl

Author

Peter Luschny, Aug 22 2018

Status

approved