A318767 G.f. satisfies: A(x) = (1+x)/(1-x) * A(x^2)*A(x^3)*A(x^4)*...*A(x^n)*... .

1, 2, 4, 8, 16, 28, 52, 88, 152, 252, 416, 664, 1076, 1684, 2636, 4060, 6248, 9444, 14292, 21312, 31748, 46796, 68804, 100200, 145784, 210240, 302520, 432428, 616716, 873972, 1236136, 1738560, 2439936, 3407924, 4749160, 6589156, 9123976, 12582620, 17316052, 23745756

Offset: 0

Author

Seiichi Manyama, Nov 04 2018

Keywords

• nonn

Comments

Convolution of A129373 and A129374. - Vaclav Kotesovec, Nov 05 2018

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A074206, A129373, A129374.

Formula

G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^A074206(k) where A074206(n) is the number of ordered factorizations of n.

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