A224735 G.f.: exp( Sum_{n>=1} binomial(2*n,n)^3 * x^n/n ).

1, 8, 140, 3616, 116542, 4316080, 175593800, 7640774080, 349626142909, 16632958651688, 816163494236860, 41069537125459360, 2110206360805542510, 110346590629125981872, 5857345961837113457864, 314962180518584299711424, 17128125582951726423704502, 940726748732537798295599280

Offset: 0

Author

Paul D. Hanna, Apr 16 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 8*x + 140*x^2 + 3616*x^3 + 116542*x^4 + 4316080*x^5 +...
where
log(A(x)) = 2^3*x + 6^3*x^2/2 + 20^3*x^3/3 + 70^3*x^4/4 + 252^3*x^5/5 + 924^3*x^6/6 + 3432^3*x^7/7 + 12870^3*x^8/8 +...+ A000984(n)^3*x^n/n +...
		

Crossrefs

Cf. A224732, A224734, A224736, A002897, A000984.

Programs

Mathematica

CoefficientList[Series[Exp[8*x*HypergeometricPFQ[{1, 1, 3/2, 3/2, 3/2}, {2, 2, 2, 2}, 64*x]], {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 27 2025 *)

PARI

{a(n)=polcoeff(exp(sum(k=1,n,binomial(2*k,k)^3*x^k/k)+x*O(x^n)),n)}
for(n=0,20,print1(a(n),", "))

Formula

Logarithmic derivative yields A002897.