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A023018
Number of partitions of n into parts of 20 kinds.
2
1, 20, 230, 1960, 13685, 82524, 443870, 2175800, 9869990, 41907380, 168012824, 640438680, 2334121995, 8171039800, 27580783270, 90058003200, 285253928790, 878572253720, 2636748302650, 7725084195240, 22130265931900, 62079251390180
OFFSET
0,2
COMMENTS
a(n) is Euler transform of A010859. - Alois P. Heinz, Oct 17 2008
FORMULA
G.f.: Product_{m>=1} 1/(1-x^m)^20.
a(0) = 1, a(n) = (20/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*20, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008
MATHEMATICA
CoefficientList[Series[1/QPochhammer[x]^20, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)
PROG
(PARI) Vec(1/eta(x)^20 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017
CROSSREFS
20th column of A144064. - Alois P. Heinz, Oct 17 2008
Sequence in context: A321674 A264876 A341394 * A073386 A022648 A004315
KEYWORD
nonn
STATUS
approved