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%I #11 Oct 05 2017 09:49:15
%S 1,-1,1,-6,24,-117,-20,93,160,-122,-156,414,459,-2038,-2486,13333,
%T 1246,2468,-8446,-13036,-4814,7848,-11453,50116,-46764,-1952,-164895,
%U 214144,249038,396600,-1598966,254048,-465174,-559712,726422,747,1067574,2897334,165438
%N G.f.: Product_{m>0} (1 - x^m + 2!*x^(2*m) - 3!*x^(3*m) + 4!*x^(4*m) - 5!*x^(5*m)).
%H Seiichi Manyama, <a href="/A293257/b293257.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(5, 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, 5, (-1)^k*k!*x^(k*m))) + O(x^50)) \\ _Michel Marcus_, Oct 04 2017
%Y Column k=5 of A293071.
%Y Cf. A293250.
%K sign
%O 0,4
%A _Seiichi Manyama_, Oct 04 2017
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