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

0,4

Links

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

Formula

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

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 *)

Crossrefs

Cf. A003483, A006950, A052565, A088026.

Sequence in context: A025012 A039938 A285846 * A332906 A361279 A096965

Adjacent sequences: A102757 A102758 A102759 * A102761 A102762 A102763

Keyword

nonn

Author

Vladeta Jovovic, Feb 10 2005

Extensions

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

Status

approved