A023009 Number of partitions of n into parts of 10 kinds.

1, 10, 65, 330, 1430, 5512, 19415, 63570, 195910, 573430, 1605340, 4322110, 11240645, 28341730, 69488650, 166096270, 387890625, 886698670, 1987322415, 4373271870, 9461022285, 20144164040, 42254620785, 87398226990, 178396331100, 359618772656, 716409453320

Offset

0,2

Comments

a(n) is Euler transform of A010692. - Alois P. Heinz, Oct 17 2008

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz)

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)^10.

a(n) ~ 5^(11/4) * exp(2 * Pi * sqrt(5*n/3)) / (64 * 3^(11/4) * n^(13/4)). - Vaclav Kotesovec, Feb 28 2015

a(0) = 1, a(n) = (10/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(10*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*10, 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)^10, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)

Crossrefs

Cf. 10th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A341387 A133715 A160458 * A169797 A073381 A092441

Adjacent sequences: A023006 A023007 A023008 * A023010 A023011 A023012

Keyword

nonn

Author

David W. Wilson

Status

approved