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%I #11 Oct 03 2017 14:32:50
%S 1,1,3,13,73,501,4050,37632,394296,4595976,58932720,823949280,
%T 12467513520,202933851120,3534322952160,65559527953920,
%U 1290129736896000,26840074522060800,588476031700677120,13560642403296468480,327603687047488051200,8278733693718654566400
%N E.g.f.: Product_{m>0} (1+x^m+x^(2*m)/2!+x^(3*m)/3!+x^(4*m)/4!+x^(5*m)/5!).
%H Seiichi Manyama, <a href="/A293197/b293197.txt">Table of n, a(n) for n = 0..444</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!, j=0..min(5, n/i))))
%p end:
%p a:= n-> n!*b(n$2):
%p seq(a(n), n=0..23); # _Alois P. Heinz_, Oct 02 2017
%Y Column k=5 of A293135.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 02 2017
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