A023010 Number of partitions of n into parts of 11 kinds.

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

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: A325733 A059625 A355053 * A303103 A258459 A320547

Adjacent sequences: A023007 A023008 A023009 * A023011 A023012 A023013

Keyword

nonn

Author

David W. Wilson

Status

approved