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A022575 Expansion of Product_{m>=1} (1+x^m)^10.

%I A022575 #22 Sep 08 2022 08:44:46
%S A022575 1,10,55,230,815,2562,7360,19700,49755,119700,276278,615130,1326965,
%T A022575 2783360,5693305,11384326,22299655,42865280,80983060,150571340,
%U A022575 275840009,498410280,889056835,1566896280,2730474975,4707724814,8035618655,13586253440,22765030080,37820087380
%N A022575 Expansion of Product_{m>=1} (1+x^m)^10.
%H A022575 Seiichi Manyama, <a href="/A022575/b022575.txt">Table of n, a(n) for n = 0..1000</a>
%F A022575 a(n) ~ (5/6)^(1/4) * exp(Pi * sqrt(10*n/3)) / (64 * n^(3/4)). - _Vaclav Kotesovec_, Mar 05 2015
%F A022575 a(0) = 1, a(n) = (10/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 03 2017
%t A022575 nmax=50; CoefficientList[Series[Product[(1+q^m)^10,{m,1,nmax}],{q,0,nmax}],q] (* _Vaclav Kotesovec_, Mar 05 2015 *)
%o A022575 (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^10)) \\ _G. C. Greubel_, Feb 26 2018
%o A022575 (Magma) Coefficients(&*[(1+x^m)^10:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 26 2018
%Y A022575 Column k=10 of A286335.
%Y A022575 Cf. A000009.
%K A022575 nonn
%O A022575 0,2
%A A022575 _N. J. A. Sloane_