A032154 Number of ways to partition n elements into pie slices of different odd sizes.

1, 1, 0, 1, 1, 1, 1, 1, 2, 3, 2, 3, 3, 5, 3, 7, 10, 9, 10, 11, 17, 15, 23, 17, 36, 45, 42, 49, 61, 77, 73, 105, 98, 159, 116, 211, 267, 289, 291, 367, 454, 493, 604, 619, 893, 795, 1175, 969, 1716, 1937, 2124, 2185, 2917, 3225, 3697, 4289, 4862, 6147

Offset

0,9

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

C. G. Bower, Transforms (2)

Index entries for sequences related to Lyndon words

Formula

"CGK" (necklace, element, unlabeled) transform of 1, 0, 1, 0, ... (odds).

G.f.: 1 + Sum_{k>=1} (k-1)! * x^(k^2) / (Product_{j=1..k} 1-x^(2*j)). - Andrew Howroyd, Sep 13 2018

Prog

(PARI) seq(n)=[subst(serlaplace(p/y), y, 1) | p <- Vec(y-1+prod(k=1, ceil(n/2), 1 + x^(2*k-1)*y + O(x*x^n)))] \\ Andrew Howroyd, Sep 13 2018
(PARI) seq(n)={Vec(1 + sum(k=1, sqrtint(n), my(r=k^2); (k-1)! * x^r / prod(j=1, k, 1 - x^(2*j) + O(x*x^(n-r)))))} \\ Andrew Howroyd, Sep 13 2018

Crossrefs

Sequence in context: A030582 A217438 A036762 * A300651 A003051 A305866

Adjacent sequences: A032151 A032152 A032153 * A032155 A032156 A032157

Keyword

nonn

Author

Christian G. Bower

Extensions

a(0)=1 prepended by Andrew Howroyd, Sep 13 2018

Status

approved