A129374 G.f. satisfies: A(x) = 1/(1-x) * A(x^2)*A(x^3)*A(x^4)*...*A(x^n)*...

1, 1, 2, 3, 6, 8, 15, 20, 35, 48, 76, 103, 166, 221, 333, 451, 671, 894, 1303, 1730, 2479, 3288, 4615, 6086, 8502, 11142, 15299, 20034, 27285, 35514, 47937, 62168, 83259, 107650, 142929, 184090, 243207, 312041, 409210, 523709, 683261, 871239, 1130703

Offset: 0

Author

Paul D. Hanna, Apr 12 2007

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A074206, A129373, A129375.

Programs

PARI

{a(n)=local(A=1+x);for(i=2,n,A=1/(1-x)*prod(n=2,i,subst(A,x,x^n+x*O(x^i)))); polcoeff(A,n)}

Formula

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

a(n) ~ exp((1 + 1/r) * (-Gamma(1+r) * Zeta(1+r) / Zeta'(r))^(1/(1+r)) * n^(r/(1+r))) * (-Gamma(1+r) * Zeta(1+r) / Zeta'(r))^(1/(10*(1+r))) / ((2*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 04 2018