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

0,2

Links

Table of n, a(n) for n=0..14.

Formula

Logarithmic derivative yields A186420.

Example

 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 +...

Prog

 (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), ", "))

Crossrefs

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

Sequence in context: A326216 A194610 A215171 * A232519 A231083 A173984

Adjacent sequences: A224733 A224734 A224735 * A224737 A224738 A224739

Keyword

nonn

Author

Paul D. Hanna, Apr 16 2013

Status

approved