login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A032153 Number of ways to partition n elements into pie slices of different sizes. 5
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

1,3

LINKS

Robert Israel, Table of n, a(n) for n = 1..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) / Prod(1<=j<=k; 1-x^j)) - Vladeta Jovovic, Sep 21 2004

MAPLE

N:= 100: # to get a(1)..a(N)

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

S:= series(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=1..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 */

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 24 17:22 EST 2018. Contains 299624 sequences. (Running on oeis4.)