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A023009
Number of partitions of n into parts of 10 kinds.
3
1, 10, 65, 330, 1430, 5512, 19415, 63570, 195910, 573430, 1605340, 4322110, 11240645, 28341730, 69488650, 166096270, 387890625, 886698670, 1987322415, 4373271870, 9461022285, 20144164040, 42254620785, 87398226990, 178396331100, 359618772656, 716409453320
OFFSET
0,2
COMMENTS
a(n) is Euler transform of A010692. - 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)
N. J. A. Sloane, Transforms
FORMULA
G.f.: Product_{m>=1} 1/(1-x^m)^10.
a(n) ~ 5^(11/4) * exp(2 * Pi * sqrt(5*n/3)) / (64 * 3^(11/4) * n^(13/4)). - Vaclav Kotesovec, Feb 28 2015
a(0) = 1, a(n) = (10/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017
G.f.: exp(10*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*10, 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)^10, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)
CROSSREFS
Cf. 10th column of A144064. - Alois P. Heinz, Oct 17 2008
Sequence in context: A341387 A133715 A160458 * A169797 A073381 A092441
KEYWORD
nonn
STATUS
approved