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A023010 Number of partitions of n into parts of 11 kinds. 3
1, 11, 77, 418, 1925, 7854, 29183, 100529, 325193, 997150, 2919411, 8207563, 22259237, 58454165, 149104450, 370410700, 898202998, 2130141651, 4949034937, 11281187225, 25262712629, 55641782779, 120661583781, 257862888360, 543532730675, 1130864017283 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is Euler transform of A010850. - Alois P. Heinz, Oct 17 2008

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for expansions of Product_{k >= 1} (1-x^k)^m

N. J. A. Sloane, Transforms

FORMULA

G.f.: Product_{m>=1} 1/(1-x^m)^11.

a(n) ~ 1331 * exp(Pi * sqrt(22*n/3)) / (2^(19/2) * 27 * n^(7/2)). - Vaclav Kotesovec, Feb 28 2015

a(0) = 1, a(n) = (11/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(11*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018

MAPLE

with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*11, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008

MATHEMATICA

nmax=50; CoefficientList[Series[Product[1/(1-x^k)^11, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)

CoefficientList[Series[1/QPochhammer[x]^11, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)

PROG

(PARI) Vec(1/eta(x)^11 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

CROSSREFS

Cf. 11th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A208599 A325733 A059625 * A303103 A258459 A320547

Adjacent sequences:  A023007 A023008 A023009 * A023011 A023012 A023013

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 17 16:58 EDT 2019. Contains 325107 sequences. (Running on oeis4.)