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A032007 "AFK" (ordered, size, unlabeled) transform of 1,2,3,4,... 1
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

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.

Sequence in context: A066964 A066967 A222450 * A091295 A215407 A084184

Adjacent sequences:  A032004 A032005 A032006 * A032008 A032009 A032010

KEYWORD

nonn

AUTHOR

Christian G. Bower

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Sep 05 2015

STATUS

approved

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Last modified October 16 05:44 EDT 2018. Contains 316259 sequences. (Running on oeis4.)