

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
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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} (k1)! * x^((k^2+3*k)/2) / (Product_{j=1..k} 1x^j).  Andrew Howroyd, Sep 13 2018


PROG

(PARI) seq(n)=[subst(serlaplace(p/y*y^0), y, 1)  p < Vec(y1+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, (k1)! * x^r / prod(j=1, k, 1  x^j + O(x*x^(nr))))))} \\ 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



