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A032012 Number of ways to partition n labeled elements into sets of different odd sizes and order the sets. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A302152 A160925 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

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Last modified October 18 05:17 EDT 2018. Contains 316304 sequences. (Running on oeis4.)