A224734 G.f.: exp( Sum_{n>=1} binomial(2*n,n)^2 * x^n/n ).

1, 4, 26, 216, 2075, 21916, 247326, 2930216, 36028117, 456089076, 5910983050, 78100285784, 1048696065394, 14275198859304, 196610207633100, 2735542102308752, 38400942393884068, 543307627503591440, 7740605626606127512, 110970838624540461472, 1599834676405793089013

Offset

0,2

Comments

The o.g.f. A(x) is the fourth power of the o.g.f. of A158266. - Peter Bala, Jun 04 2015

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..800

Formula

Logarithmic derivative yields A002894.

Example

G.f.: A(x) = 1 + 4*x + 26*x^2 + 216*x^3 + 2075*x^4 + 21916*x^5 + 247326*x^6 +...
where
log(A(x)) = 2^2*x + 6^2*x^2/2 + 20^2*x^3/3 + 70^2*x^4/4 + 252^2*x^5/5 + 924^2*x^6/6 + 3432^2*x^7/7 + 12870^2*x^8/8 +...+ A000984(n)^2*x^n/n +...

Prog

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

Crossrefs

Cf. A224732, A224735, A224736, A002894, A000984, A158266.

Sequence in context: A306028 A164101 A048351 * A143436 A135884 A364973

Adjacent sequences: A224731 A224732 A224733 * A224735 A224736 A224737

Keyword

nonn

Author

Paul D. Hanna, Apr 16 2013

Status

approved