cp's OEIS Frontend

A096619 Number of partitions of a 2*n-element set with exactly two odd blocks.

%I A096619 #12 May 13 2015 03:49:43
%S A096619 1,10,136,2500,59671,1786060,65222431,2843052040,145349748316,
%T A096619 8590361117290,579887365929301,44257224641241160,3785653479578940061,
%U A096619 360188281690273321750,37868568207290527576096,4373779619483505303462160,552095790104596359907313731
%N A096619 Number of partitions of a 2*n-element set with exactly two odd blocks.
%H A096619 Alois P. Heinz, <a href="/A096619/b096619.txt">Table of n, a(n) for n = 1..250</a>
%F A096619 E.g.f.: 1/2*exp(cosh(x)-1)*(sinh(x))^2. More generally, number of partitions of an n-element set with exactly k odd blocks is 1/k!*exp(cosh(x)-1)*(sinh(x))^k.
%p A096619 with(combinat):
%p A096619 b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
%p A096619       `if`(i<1 or t<0, 0, add(multinomial(n, n-i*j, i$j)/j!*
%p A096619       b(n-i*j, i-1, t-`if`(irem(i, 2)=1, j, 0) ), j=0..n/i)))
%p A096619     end:
%p A096619 a:= n-> b(2*n$2, 2):
%p A096619 seq(a(n), n=1..20);  # _Alois P. Heinz_, Mar 08 2015
%t A096619 multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i<1 || t<0, 0, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*b[n-i*j, i-1, t-If[Mod[i, 2] == 1, j, 0]], {j, 0, n/i}]]]; a[n_] := b[2*n, 2*n, 2]; Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, May 13 2015, after _Alois P. Heinz_ *)
%Y A096619 Cf. A005046.
%K A096619 easy,nonn
%O A096619 1,2
%A A096619 _Vladeta Jovovic_, Aug 14 2004
%E A096619 More terms from _Emeric Deutsch_, Nov 16 2004