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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-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 * A256824 A176558 A243360 Adjacent sequences:  A032010 A032011 A032012 * A032014 A032015 A032016 KEYWORD nonn AUTHOR EXTENSIONS a(0)=1 prepended by Alois P. Heinz, May 11 2016 STATUS approved

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Last modified October 24 01:08 EDT 2018. Contains 316541 sequences. (Running on oeis4.)