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A022575
Expansion of Product_{m>=1} (1+x^m)^10.
2
1, 10, 55, 230, 815, 2562, 7360, 19700, 49755, 119700, 276278, 615130, 1326965, 2783360, 5693305, 11384326, 22299655, 42865280, 80983060, 150571340, 275840009, 498410280, 889056835, 1566896280, 2730474975, 4707724814, 8035618655, 13586253440, 22765030080, 37820087380
OFFSET
0,2
LINKS
FORMULA
a(n) ~ (5/6)^(1/4) * exp(Pi * sqrt(10*n/3)) / (64 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015
a(0) = 1, a(n) = (10/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017
MATHEMATICA
nmax=50; CoefficientList[Series[Product[(1+q^m)^10, {m, 1, nmax}], {q, 0, nmax}], q] (* Vaclav Kotesovec, Mar 05 2015 *)
PROG
(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1+q^n)^10)) \\ G. C. Greubel, Feb 26 2018
(Magma) Coefficients(&*[(1+x^m)^10:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 26 2018
CROSSREFS
Column k=10 of A286335.
Cf. A000009.
Sequence in context: A341223 A337631 A249460 * A202481 A348663 A169720
KEYWORD
nonn
STATUS
approved