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%I #14 Oct 05 2017 09:49:08
%S 1,-1,1,-6,24,3,-20,-27,40,-2,-36,-186,579,-118,274,-347,46,-892,74,
%T -76,3106,-3192,-1013,-4844,12276,-752,2145,-656,11198,-11160,-2246,
%U -38752,32106,-24272,42182,-7533,36054,-78906,-4482,-164462,381837,-174346,21356,-114910
%N G.f.: Product_{m>0} (1 - x^m + 2!*x^(2*m) - 3!*x^(3*m) + 4!*x^(4*m)).
%H Seiichi Manyama, <a href="/A293256/b293256.txt">Table of n, a(n) for n = 0..500</a>
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(b(n-i*j, i-1)*j!*(-1)^j, j=0..min(4, n/i))))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..60); # _Alois P. Heinz_, Oct 04 2017
%o (PARI) Vec(prod(m=1, 50, 1+sum(k=1, 4, (-1)^k*k!*x^(k*m))) + O(x^50)) \\ _Michel Marcus_, Oct 04 2017
%Y Column k=4 of A293071.
%Y Cf. A289486.
%K sign
%O 0,4
%A _Seiichi Manyama_, Oct 04 2017
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