A115278 Number of partitions of {1,...,2*n} into even sized blocks such that no block size is repeated.

1, 1, 1, 16, 29, 256, 14422, 49141, 490429, 10758400, 1797335306, 9458619391, 133756636598, 2528529510391, 137864810180749, 53441183229799381, 410251032050409469, 7615997734377068128, 167055180095977694194, 6741819165851219788075, 738863335901972011745434

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..370

Formula

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)!).

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-2), j=0..min(1, n/i))))
    end:
a:= n-> b(2*n$2):
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 08 2015

Mathematica

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 *)

Crossrefs

Cf. A005046, A007837, A032310, A115277.

Sequence in context: A246345 A054314 A222545 * A228664 A359935 A217715

Adjacent sequences: A115275 A115276 A115277 * A115279 A115280 A115281

Keyword

nonn

Author

Christian G. Bower, Jan 18 2006

Status

approved