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

Author

David W. Wilson

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

PARI

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

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