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G.f.: Product_{m>0} (1 + x^m + 2!*x^(2*m) + 3!*x^(3*m) + 4!*x^(4*m)).
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%I #36 Oct 04 2017 09:51:41

%S 1,1,3,8,30,13,48,61,142,170,378,430,1099,872,1304,2305,3626,4042,

%T 6900,8086,13634,17628,24915,29524,53998,51718,74953,96996,150104,

%U 172292,234938,296472,416064,504132,690826,812625,1184134,1378774,1823778,2264576,3115051

%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="/A289486/b289486.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!, j=0..min(4, n/i))))

%p end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..50); # _Alois P. Heinz_, Oct 04 2017

%Y Column k=4 of A293202.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 03 2017