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A115278 Number of partitions of {1,...,2*n} into even sized blocks such that no block size is repeated. 2
1, 1, 1, 16, 29, 256, 14422, 49141, 490429, 10758400, 1797335306, 9458619391, 133756636598, 2528529510391, 137864810180749, 53441183229799381, 410251032050409469, 7615997734377068128, 167055180095977694194, 6741819165851219788075, 738863335901972011745434 (list; graph; refs; listen; history; text; internal format)
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 A217715 A064634

Adjacent sequences:  A115275 A115276 A115277 * A115279 A115280 A115281

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 18 2006

STATUS

approved

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Last modified February 16 20:45 EST 2019. Contains 320189 sequences. (Running on oeis4.)