A129375 E.g.f. satisfies: A(x) = exp(x) * A(x^2)*A(x^3)*A(x^4)*...*A(x^n)*...
1, 1, 3, 13, 97, 621, 6571, 58633, 779073, 9317017, 138628531, 1977676581, 37384244833, 620735382853, 12434855135067, 245117537189281, 5651550278494081, 123266430844431153, 3128700944169196003
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..260
Programs
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PARI
{a(n)=local(A=1+x);for(i=2,n,A=exp(x+x*O(x^n))*prod(n=2,i,subst(A,x,x^n+x*O(x^i)))); n!*polcoeff(A,n)}
Formula
E.g.f.: A(x) = exp( Sum_{n>=1} A074206(n)*x^n ) where A074206(n) equals the number of ordered factorizations of n.
a(n) ~ n! * exp(2/5 + (1 + 1/r) * (-Gamma(1+r) / Zeta'(r))^(1/(1+r)) * n^(r/(1+r))) * (-Gamma(1+r) / Zeta'(r))^(1/(2*(1+r))) / (sqrt(2*Pi*(1+r)) * n^((2+r)/(2*(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
Extensions
PARI program fixed by Vaclav Kotesovec, Feb 26 2014