A023005 Number of partitions of n into parts of 6 kinds.

1, 6, 27, 98, 315, 918, 2492, 6372, 15525, 36280, 81816, 178794, 380051, 788004, 1597725, 3174210, 6190182, 11867310, 22395359, 41650050, 76413078, 138421358, 247783113, 438616728, 768291650, 1332444330, 2289213495, 3898064226, 6581591157, 11023247880

Offset

0,2

Comments

a(n) is Euler transform of A010722. - Alois P. Heinz, Oct 17 2008

Links

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

Roland Bacher, P. De La Harpe, Conjugacy growth series of some infinitely generated groups. 2016, hal-01285685v2.

P. Nataf, M. Lajkó, A. Wietek, K. Penc, F. Mila, A. M. Läuchli, Chiral spin liquids in triangular lattice SU (N) fermionic Mott insulators with artificial gauge fields, arXiv preprint arXiv:1601.00958 [cond-mat.quant-gas], 2016.

N. J. A. Sloane, Transforms

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

Formula

G.f.: Product_{m>=1} 1/(1-x^m)^6.

a(n) ~ exp(2 * Pi * sqrt(n)) / (16 * n^(9/4)). - Vaclav Kotesovec, Feb 28 2015

a(0) = 1, a(n) = (6/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 26 2017

G.f.: exp(6*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*6, 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)^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)

Crossrefs

Cf. 6th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A182821 A277283 A160533 * A001874 A009061 A012320

Adjacent sequences: A023002 A023003 A023004 * A023006 A023007 A023008

Keyword

nonn

Author

David W. Wilson

Status

approved