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A032013 Number of ways to partition n labeled elements into sets of different sizes of at least 2 and order the sets. 1
1, 0, 1, 1, 1, 21, 31, 113, 169, 8053, 15871, 71325, 300147, 816401, 63105953, 161203747, 856049593, 4050514725, 25570388671, 80377109117, 12126315199099, 36747628912981, 233849676829957, 1239662165799711, 8321234529548651, 59953576690379081 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..673

C. G. Bower, Transforms (2)

FORMULA

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

MAPLE

b:= proc(n, i, p) option remember;

      `if`(n=0, p!, `if`(i<2, 0, b(n, i-1, p)+

      `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(n, i))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..30);  # Alois P. Heinz, May 11 2016

MATHEMATICA

b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 2, 0, b[n, i - 1, p] + If[i > n, 0, b[n - i, i - 1, p + 1]*Binomial[n, i]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Feb 27 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A032011.

Sequence in context: A104297 A106324 A208293 * A256824 A176558 A243360

Adjacent sequences:  A032010 A032011 A032012 * A032014 A032015 A032016

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 February 23 23:56 EST 2018. Contains 299595 sequences. (Running on oeis4.)