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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.

%I A318257 #9 Aug 26 2018 05:31:22
%S A318257 1,0,1,0,1,126,0,1,3003,126126,0,1,107882,23279256,488864376,0,1,
%T A318257 3321890,5319906900,412275623760,5194672859376,0,1,107746281,
%U A318257 1394769716340,369277150181940,14687937509885640,123378675083039376
%N 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.
%e A318257 [0] [1]
%e A318257 [1] [0, 1]
%e A318257 [2] [0, 1,     126]
%e A318257 [3] [0, 1,    3003,     126126]
%e A318257 [4] [0, 1,  107882,   23279256,    488864376]
%e A318257 [5] [0, 1, 3321890, 5319906900, 412275623760, 5194672859376]
%p A318257 CL := p -> PolynomialTools:-CoefficientList(p, x):
%p A318257 FL := p -> ListTools:-Flatten(p):
%p A318257 f := z -> (1/5)*(exp(z)+2*(+exp(1/4*z*(5^(1/2)-1))*cos(1/4*z*2^(1/2)*
%p A318257 (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)))):
%p A318257 gf := exp(x*(f(z)-1)): ser := series(gf, z, 48):
%p A318257 FL([seq(CL(sort(expand((5*n)!*coeff(ser, z, n*5)), [x], ascending)),n=0..7)]);
%Y A318257 Cf. A048993 (m=1), A156289 (m=2), A291451 (m=3), A291452 (m=4), this seq (m=5).
%K A318257 nonn,tabl
%O A318257 0,6
%A A318257 _Peter Luschny_, Aug 22 2018