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A023008
Number of partitions of n into parts of 9 kinds.
4
1, 9, 54, 255, 1035, 3753, 12483, 38709, 113265, 315445, 841842, 2164185, 5382276, 12994290, 30543210, 70066809, 157199805, 345552183, 745377215, 1579915080, 3294664578, 6766656315, 13700560491, 27370137195, 53991639855, 105242612526, 202837976145
OFFSET
0,2
COMMENTS
a(n) is Euler transform of A010734. - 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)
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
FORMULA
a(n) ~ 3^(5/2) * exp(Pi * sqrt(6*n)) / (256 * n^3). - Vaclav Kotesovec, Feb 28 2015
a(0) = 1, a(n) = (9/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017
G.f.: exp(9*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*9, 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)^9, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)
CROSSREFS
Cf. 9th column of A144064. - Alois P. Heinz, Oct 17 2008
Sequence in context: A059597 A327387 A282920 * A079817 A169796 A359722
KEYWORD
nonn
STATUS
approved