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