A032012 Number of ways to partition n labeled elements into sets of different odd sizes and order the sets.

1, 1, 0, 1, 8, 1, 12, 1, 128, 3025, 260, 7921, 2048, 78937, 4760, 2375101, 138411008, 9837697, 588189972, 96605425, 7353141248, 1752111145, 151280741480, 9294316285, 12191175684608, 1413604888888801, 75955683963432, 9022098736088101, 1170150933402368

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..742

C. G. Bower, Transforms (2)

Formula

"AGJ" (ordered, elements, labeled) transform of 1, 0, 1, 0, ...(odds).

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`(i<1, 0, b(n, i-2, p)+
      `if`(i>n, 0, b(n-i, i-2, p+1)*binomial(n, i))))
    end:
a:= n-> b(n, n-1+irem(n, 2), 0):
seq(a(n), n=0..30);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n==0, p!, If[i<1, 0, b[n, i-2, p] + If[i>n, 0, b[n-i, i-2, p+1]*Binomial[n, i]]]]; a[n_] := b[n, n-1+Mod[n, 2], 0]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 27 2017, translated from Maple *)

Prog

(PARI) seq(n)=[subst(serlaplace(y^0*p), y, 1) | p <- Vec(serlaplace(prod(k=1, ceil(n/2), 1 + x^(2*k-1)*y/(2*k-1)! + O(x*x^n))))] \\ Andrew Howroyd, Sep 13 2018

Crossrefs

Sequence in context: A345059 A348973 A099614 * A092702 A070475 A045771

Adjacent sequences: A032009 A032010 A032011 * A032013 A032014 A032015

Keyword

nonn

Author

Christian G. Bower

Extensions

a(0)=1 prepended by Alois P. Heinz, May 11 2016

Status

approved