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URL: https://oeis.org/A032007

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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
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
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
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Sep 05 2015
STATUS
approved