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A032154 Number of ways to partition n elements into pie slices of different odd sizes. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A031248 A030582 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

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Last modified October 17 01:09 EDT 2018. Contains 316275 sequences. (Running on oeis4.)