A032013 - OEIS

%I #19 Sep 13 2018 18:33:10

%S 1,0,1,1,1,21,31,113,169,8053,15871,71325,300147,816401,63105953,

%T 161203747,856049593,4050514725,25570388671,80377109117,

%U 12126315199099,36747628912981,233849676829957,1239662165799711,8321234529548651,59953576690379081

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

%H Alois P. Heinz, <a href="/A032013/b032013.txt">Table of n, a(n) for n = 0..673</a>

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

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

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

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

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

%p     end:

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

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, May 11 2016

%t 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_ *)

%o (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

%Y Cf. A032011.

%K nonn

%O 0,6

%A _Christian G. Bower_

%E a(0)=1 prepended by _Alois P. Heinz_, May 11 2016