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