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A032155 Number of ways to partition n elements into pie slices of different sizes other than one. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 02:46 EDT 2018. Contains 316431 sequences. (Running on oeis4.)