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 A032007 "AFK" (ordered, size, unlabeled) transform of 1,2,3,4,... 4
 1, 1, 2, 7, 10, 25, 68, 111, 208, 435, 1218, 1773, 3586, 6077, 12156, 31961, 47624, 86825, 151962, 265525, 469610, 1242607, 1750108, 3217663, 5263928, 9205197, 14713474, 26440503, 63610938, 90877893, 159360628, 258871127, 431309688, 687140639, 1134231986 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sum of products of parts in all compositions of n into distinct parts. - Vladeta Jovovic, Feb 21 2005 Number of compositions of n into distinct parts if there are i kinds of part i. a(3) = 7: 3, 3', 3'', 21, 2'1, 12, 12'. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..5000 C. G. Bower, Transforms (2) MAPLE b:= proc(n, i, p) option remember;       `if`(n=0, p!, `if`(i<1, 0, b(n, i-1, p)+       `if`(i>n, 0, i*b(n-i, i-1, p+1))))     end: a:= n-> b(n\$2, 0): seq(a(n), n=0..40);  # Alois P. Heinz, Sep 05 2015 MATHEMATICA b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 1, 0, b[n, i - 1, p] + If[i > n, 0, i*b[n - i, i - 1, p + 1]]]]; a[n_] := b[n, n, 0]; a /@ Range[0, 40] (* Jean-François Alcover, Sep 11 2019, after Alois P. Heinz *) PROG (PARI) seq(n)={apply(p->subst(serlaplace(p), y, 1), Vec(prod(k=1, n, 1 + k*x^k*y + O(x*x^n))))} \\ Andrew Howroyd, Jun 21 2018 CROSSREFS Cf. A022629. Cf. A032005, A032006, A032008. Sequence in context: A066964 A066967 A222450 * A091295 A215407 A084184 Adjacent sequences:  A032004 A032005 A032006 * A032008 A032009 A032010 KEYWORD nonn AUTHOR EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Sep 05 2015 STATUS approved

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Last modified May 27 04:33 EDT 2020. Contains 334649 sequences. (Running on oeis4.)