A293195 E.g.f.: Product_{m>0} (1+x^m+x^(2*m)/2!+x^(3*m)/3!).

1, 1, 3, 13, 72, 500, 4020, 37380, 389760, 4546080, 58363200, 814968000, 12301027200, 200216016000, 3484710028800, 64639070496000, 1270187702784000, 26414731639296000, 578733086131200000, 13328586071184384000, 321801976039864320000, 8127599117746268160000

Offset: 0

Author

Seiichi Manyama, Oct 02 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..444

Crossrefs

Column k=3 of A293135.

Cf. A001935.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1)/j!, j=0..min(3, n/i))))
    end:
a:= n-> n!*b(n$2):
seq(a(n), n=0..23);  # Alois P. Heinz, Oct 02 2017