A115277 Number of partitions of {1,...,n} into blocks such that no even sized block is repeated.

1, 1, 2, 5, 12, 37, 143, 562, 2320, 10941, 54865, 283890, 1604155, 9558226, 58668223, 384572975, 2631778832, 18576630237, 137919691717, 1060303298138, 8415786131309, 69538205444478, 591734670548037, 5194542789203877, 47127033586211659, 438972204436025198

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

E.g.f.: exp(sinh(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-1), j=0..min(
       `if`(irem(i, 2)=0, 1, n), n/i))))
    end:
a:= n-> b(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-1], {j, 0, Min[If[Mod[i, 2]==0, 1, n], n/i]}]]]; a[n_] :=  b[n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Oct 25 2015, after Alois P. Heinz *)

Crossrefs

Cf. A001935, A115275, A115276, A115278.

Sequence in context: A024717 A003724 A138314 * A130221 A036782 A050237

Adjacent sequences: A115274 A115275 A115276 * A115278 A115279 A115280

Keyword

nonn

Author

Christian G. Bower, Jan 18 2006

Status

approved