login
E.g.f.: Product_{m>0} (1+x^m+x^(2*m)/2!+x^(3*m)/3!).
2

%I #14 Oct 03 2017 10:46:34

%S 1,1,3,13,72,500,4020,37380,389760,4546080,58363200,814968000,

%T 12301027200,200216016000,3484710028800,64639070496000,

%U 1270187702784000,26414731639296000,578733086131200000,13328586071184384000,321801976039864320000,8127599117746268160000

%N E.g.f.: Product_{m>0} (1+x^m+x^(2*m)/2!+x^(3*m)/3!).

%H Seiichi Manyama, <a href="/A293195/b293195.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(3, 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=3 of A293135.

%Y Cf. A001935.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 02 2017