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 A023008 Number of partitions of n into parts of 9 kinds. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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: A289254 A059597 A282920 * A079817 A169796 A027472 Adjacent sequences:  A023005 A023006 A023007 * A023009 A023010 A023011 KEYWORD nonn AUTHOR STATUS approved

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Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)