A032008 "AFK" (ordered, size, unlabeled) transform of 1,3,5,7,...

1, 1, 3, 11, 17, 53, 161, 285, 569, 1459, 4699, 7177, 15631, 28229, 66883, 211311, 319929, 627705, 1163049, 2150209, 4422225, 14320583, 20392019, 39962165, 68618087, 126643545, 212615483, 433704811, 1312156393, 1864959757, 3502343041, 5919183485, 10364053441

Offset

0,3

Comments

Number of compositions of n into distinct parts if there are (2i-1) kinds of part i. a(3) = 11: 3, 3', 3'', 3''', 3'''', 21, 2'1, 2''1, 12, 12', 12''. - Alois P. Heinz, Sep 05 2015

Links

Alois P. Heinz, Table of n, a(n) for n = 0..4000

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, (2*i-1)*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, (2 i - 1)*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 + (2*k-1)*x^k*y + O(x*x^n))))} \\ Andrew Howroyd, Jun 21 2018

Crossrefs

Cf. A032005, A032006, A032007.

Sequence in context: A078116 A245045 A127996 * A061368 A145701 A072982

Adjacent sequences: A032005 A032006 A032007 * A032009 A032010 A032011

Keyword

nonn

Author

Christian G. Bower

Extensions

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

Status

approved