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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 (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 Index entries for expansions of Product_{k >= 1} (1-x^k)^m 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 Adjacent sequences: A023005 A023006 A023007 * A023009 A023010 A023011 KEYWORD nonn AUTHOR David W. Wilson STATUS approved

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Last modified December 5 19:51 EST 2023. Contains 367593 sequences. (Running on oeis4.)