A224732 G.f.: exp( Sum_{n>=1} binomial(2*n,n)^n * x^n/n ).

1, 2, 20, 2704, 6008032, 203263062688, 103724721990326528, 801185400238209125917312, 94088900962948953837864576996352, 168691065596220817138271126002845218561536, 4634314586972355372645450331391809316221983940020224

Offset: 0

Author

Paul D. Hanna, Apr 16 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 20*x^2 + 2704*x^3 + 6008032*x^4 + 203263062688*x^5 +...
where
log(A(x)) = 2*x + 6^2*x^2/2 + 20^3*x^3/3 + 70^4*x^4/4 + 252^5*x^5/5 + 924^6*x^6/6 + 3432^7*x^7/7 + 12870^8*x^8/8 +...+ A000984(n)^n*x^n/n +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A200002, A224733, A201556, A224734, A224735, A224736, A000984.

Programs

PARI

{a(n)=polcoeff(exp(sum(k=1,n,binomial(2*k,k)^k*x^k/k)+x*O(x^n)),n)}
for(n=0,20,print1(a(n),", "))

Formula

Logarithmic derivative yields A224733.

a(n) ~ exp(-1/8) * 2^(2*n^2) / (Pi^(n/2) * n^(1 + n/2)). - Vaclav Kotesovec, Jan 26 2015

a(n) ~ (binomial(2*n,n))^n / n. - Vaclav Kotesovec, Jan 26 2015