A102760 Number of partitions of n-set into "lists", in which every even list appears an even number of times, cf. A000262.

1, 1, 1, 7, 37, 241, 1381, 13231, 140617, 1483777, 16211881, 217551511, 3384215341, 50221272817, 782154787597, 13913712591871, 272739557719441, 5282625708305281, 106588332600443857, 2354480141600267047, 56238135934525073461, 1338131691952924913521

Offset: 0

Author

Vladeta Jovovic, Feb 10 2005

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..445

Crossrefs

Cf. A003483, A006950, A052565, A088026.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(`if`(i::even and j::odd, 0, b(n-i*j, i-1)*
      multinomial(n, n-i*j, i$j)/j!*i!^j), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);  # Alois P. Heinz, May 10 2016

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[If[EvenQ[i] && OddQ[j], 0, b[n-i*j, i- 1] * multinomial[n, Join[{n - i*j}, Array[i &, j]]]/j!*i!^j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 05 2017, after Alois P. Heinz *)

Formula

E.g.f.: exp(x/(1-x^2))*Product_{k>0} cosh(x^(2*k)).

Extensions

a(0)=1 prepended by Alois P. Heinz, May 10 2016