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A289485 G.f.: Product_{m>0} (1 + x^m + 2!*x^(2*m) + 3!*x^(3*m)).

%I A289485 #43 Oct 04 2017 14:07:33
%S A289485 1,1,3,8,6,13,24,37,46,98,90,142,235,296,392,601,746,1018,1428,1702,
%T A289485 2258,3132,3891,5044,6766,8134,10681,13812,16952,20996,27986,33144,
%U A289485 41376,52500,64066,79401,99718,119590,147162,181880,220339,266662,329342,391736
%N A289485 G.f.: Product_{m>0} (1 + x^m + 2!*x^(2*m) + 3!*x^(3*m)).
%H A289485 Seiichi Manyama, <a href="/A289485/b289485.txt">Table of n, a(n) for n = 0..500</a>
%p A289485 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A289485       add(b(n-i*j, i-1)*j!, j=0..min(3, n/i))))
%p A289485     end:
%p A289485 a:= n-> b(n$2):
%p A289485 seq(a(n), n=0..50);  # _Alois P. Heinz_, Oct 04 2017
%o A289485 (PARI) Vec(prod(m=1, 50, 1+x^m+2*x^(2*m)+6*x^(3*m)) + O(x^50)) \\ _Michel Marcus_, Oct 04 2017
%Y A289485 Column k=3 of A293202.
%K A289485 nonn
%O A289485 0,3
%A A289485 _Seiichi Manyama_, Oct 03 2017