|
%I #24 Nov 05 2018 14:09:30
%S 1,2,4,8,16,28,52,88,152,252,416,664,1076,1684,2636,4060,6248,9444,
%T 14292,21312,31748,46796,68804,100200,145784,210240,302520,432428,
%U 616716,873972,1236136,1738560,2439936,3407924,4749160,6589156,9123976,12582620,17316052,23745756
%N G.f. satisfies: A(x) = (1+x)/(1-x) * A(x^2)*A(x^3)*A(x^4)*...*A(x^n)*... .
%C Convolution of A129373 and A129374. - _Vaclav Kotesovec_, Nov 05 2018
%H Vaclav Kotesovec, <a href="/A318767/b318767.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^A074206(k) where A074206(n) is the number of ordered factorizations of n.
%F a(n) ~ exp((1+r) * ((2^(1+r) - 1) * Gamma(1+r) * Zeta(1+r))^(1/(1+r)) * n^(r/(1+r)) / (r * 2^(r/(1+r)) * (-Zeta'(r))^(1/(1+r)))) * (-2*(2^(1+r) - 1) * Gamma(1+r) * Zeta(1+r) / Zeta'(r))^(1/(10*(1+r))) / (2^(7/25) * Pi^(29/50) * sqrt(1+r) * n^((6+5*r)/(10*(1+r)))), where r = A107311 = 1.7286472389981836181351... is the root of the equation Zeta(r) = 2, Zeta'(r) = -1/A247667. - _Vaclav Kotesovec_, Nov 05 2018
%Y Cf. A074206, A129373, A129374.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 04 2018
|
