A032155 Number of ways to partition n elements into pie slices of different sizes other than one.

1, 0, 1, 1, 1, 2, 2, 3, 3, 6, 6, 9, 11, 14, 22, 27, 35, 46, 62, 73, 119, 138, 190, 239, 323, 402, 522, 753, 927, 1218, 1574, 2039, 2599, 3390, 4154, 6013, 7247, 9574, 12026, 15807, 19615, 25598, 31850, 40293, 54795, 67530, 86202, 109851

Offset

0,6

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 0, 1, 1, 1, ...

G.f.: 1 + Sum_{k>=1} (k-1)! * x^((k^2+3*k)/2) / (Product_{j=1..k} 1-x^j). - Andrew Howroyd, Sep 13 2018

Prog

(PARI) seq(n)=[subst(serlaplace(p/y*y^0), y, 1) | p <- Vec(y-1+prod(k=2, n, 1 + x^k*y + O(x*x^n)))] \\ Andrew Howroyd, Sep 13 2018
(PARI) seq(n)={Vec(1 + sum(k=1, n, my(r=(k^2+3*k)/2); if(r<=n, (k-1)! * x^r / prod(j=1, k, 1 - x^j + O(x*x^(n-r))))))} \\ Andrew Howroyd, Sep 13 2018

Crossrefs

Sequence in context: A213332 A133392 A101199 * A116932 A240579 A292225

Adjacent sequences: A032152 A032153 A032154 * A032156 A032157 A032158

Keyword

nonn

Author

Christian G. Bower

Extensions

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

Status

approved