A115278 - OEIS

%I #8 Jan 22 2016 08:06:45

%S 1,1,1,16,29,256,14422,49141,490429,10758400,1797335306,9458619391,

%T 133756636598,2528529510391,137864810180749,53441183229799381,

%U 410251032050409469,7615997734377068128,167055180095977694194,6741819165851219788075,738863335901972011745434

%N Number of partitions of {1,...,2*n} into even sized blocks such that no block size is repeated.

%H Alois P. Heinz, <a href="/A115278/b115278.txt">Table of n, a(n) for n = 0..370</a>

%F E.g.f.: B(x) of b(n) where b(2*n)=a(n), b(2*n+1)=0. B(x)=Product {m >= 1} (1+x^(2*m)/(2*m)!).

%p with(combinat):

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(

%p       multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-2), j=0..min(1, n/i))))

%p     end:

%p a:= n-> b(2*n$2):

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 08 2015

%t multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Array[i &, j]]]/j!* b[n - i*j, i - 2], {j, 0, Min[1, n/i]}]]]; a[n_] := b[2 n, 2 n]; Table[ a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jan 22 2016, after _Alois P. Heinz_ *)

%Y Cf. A005046, A007837, A032310, A115277.

%K nonn

%O 0,4

%A _Christian G. Bower_, Jan 18 2006