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A032153 Number of ways to partition n elements into pie slices of different sizes. 6
1, 1, 1, 2, 2, 3, 5, 6, 8, 11, 19, 22, 32, 41, 57, 92, 114, 155, 209, 280, 364, 587, 707, 984, 1280, 1737, 2213, 2990, 4390, 5491, 7361, 9650, 12708, 16451, 21567, 27506, 40100, 49201, 65701, 84128, 111278, 140595, 184661, 232356, 300680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Robert Israel, Table of n, a(n) for n = 0..2000

C. G. Bower, Transforms (2)

Index entries for sequences related to Lyndon words

FORMULA

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

G.f.: Sum_{k >= 1} (k-1)! * x^((k^2+k)/2) / (Product_{j=1..k} 1-x^j). - Vladeta Jovovic, Sep 21 2004

MAPLE

N:= 100: # to get a(0)..a(N)

K:= floor(isqrt(1+8*N)/2):

S:= series(1+add((k-1)!*x^((k^2+k)/2)/mul(1-x^j, j=1..k), k=1..K), x, N+1):

seq(coeff(S, x, j), j=0..N); # Robert Israel, Jul 15 2016

MATHEMATICA

max=50; s=Sum[(x^(k(k+1)/2-1)*(k-1)!)/QPochhammer[x, x, k], {k, 1, max}] + O[x]^max; CoefficientList[s, x] (* Jean-Fran├žois Alcover, Jan 19 2016 *)

PROG

(PARI)

N=66;  q='q+O('q^N);

gf=sum(n=1, N, (n-1)!*q^(n*(n+1)/2) / prod(k=1, n, 1-q^k ) );

Vec(gf)

/* Joerg Arndt, Oct 20 2012 */

(PARI) seq(n)=[subst(serlaplace(p/y), y, 1) | p <- Vec(y-1+prod(k=1, n, 1 + x^k*y + O(x*x^n)))] \\ Andrew Howroyd, Sep 13 2018

CROSSREFS

Cf. A032020.

Sequence in context: A084783 A265853 A129838 * A116465 A117356 A017819

Adjacent sequences:  A032150 A032151 A032152 * A032154 A032155 A032156

KEYWORD

nonn,nice

AUTHOR

Christian G. Bower

EXTENSIONS

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

STATUS

approved

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Last modified October 18 05:17 EDT 2018. Contains 316304 sequences. (Running on oeis4.)