A032013 Number of ways to partition n labeled elements into sets of different sizes of at least 2 and order the sets.

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

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-François Alcover, Feb 27 2017, after Alois P. Heinz *)

Prog

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

Crossrefs

Cf. A032011.

Sequence in context: A104297 A106324 A208293 * A324489 A256824 A176558

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