A224736 G.f.: exp( Sum_{n>=1} binomial(2*n,n)^4 * x^n/n ).

1, 16, 776, 64384, 7151460, 947788608, 141137282720, 22814994697728, 3918995299504938, 705339416079749024, 131725296229995045840, 25348575698532710671104, 5000341179482293108254824, 1007144334380887781805059200, 206487157000689985136888031296

Offset: 0

Author

Paul D. Hanna, Apr 16 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 16*x + 776*x^2 + 64384*x^3 + 7151460*x^4 + 947788608*x^5 +...
where
log(A(x)) = 2^4*x + 6^4*x^2/2 + 20^4*x^3/3 + 70^4*x^4/4 + 252^4*x^5/5 + 924^4*x^6/6 + 3432^4*x^7/7 + 12870^4*x^8/8 +...+ A000984(n)^4*x^n/n +...
		

Crossrefs

Cf. A224732, A224734, A224735, A186420, A000984.

Programs

Mathematica

CoefficientList[Series[Exp[16*x*HypergeometricPFQ[{1, 1, 3/2, 3/2, 3/2, 3/2}, {2, 2, 2, 2, 2}, 256*x]], {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 27 2025 *)

PARI

{a(n)=polcoeff(exp(sum(k=1,n,binomial(2*k,k)^4*x^k/k)+x*O(x^n)),n)}
for(n=0,20,print1(a(n),", "))

Formula

Logarithmic derivative yields A186420.