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A023007 Number of partitions of n into parts of 8 kinds. 3
1, 8, 44, 192, 726, 2464, 7704, 22528, 62337, 164560, 417140, 1020416, 2418710, 5573568, 12520744, 27484160, 59068372, 124505880, 257770964, 524871424, 1052316364, 2079491744, 4053978040, 7803219968, 14840711765, 27907041392, 51917588800, 95608651776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is Euler transform of A010731. - 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)

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

a(n) ~ exp(4 * Pi * sqrt(n/3)) / (sqrt(2) * 3^(9/4) * n^(11/4)). - Vaclav Kotesovec, Feb 28 2015

a(0) = 1, a(n) = (8/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

MAPLE

with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*8, 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)^8, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)

CROSSREFS

Cf. 8th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A160521 A277958 A283077 * A169795 A073380 A273603

Adjacent sequences:  A023004 A023005 A023006 * A023008 A023009 A023010

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified April 30 08:33 EDT 2017. Contains 285645 sequences.