A136550 a(n) = C(2^n + 2*n, n) * 2^n / (2^n + 2*n); a(n) = coefficient of x^n in Catalan(x)^(2^n).

1, 2, 14, 208, 7084, 648128, 184100160, 179176044032, 630345044388960, 8204566969800002560, 398166559635173802124288, 72163718410109803095272136704, 48857217948449362973220983661357056

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

G.f.: A(x) = Sum_{n>=0} log( Catalan(2^n*x) )^n / n! where Catalan(x) = 2/(1+sqrt(1-4*x)).

Example

G.f.: A(x) = 1 + 2*x + 14*x^2 + 208*x^3 + 7084*x^4 + 648128*x^5 +...
A(x) = Sum_{n>=0} log(1 +1*2^n*x +2*4^n*x^2 +5*8^n*x^3 +14*16^n*x^4 +...)^n/n!.

Prog

(PARI) a(n)=binomial(2^n + 2*n, n)*2^n/(2^n + 2*n)
(PARI) a(n)=polcoeff((2/(1+sqrt(1-4*x +x*O(x^n))))^(2^n), n)
(PARI) a(n)=polcoeff(sum(k=0, n, log( 2/(1+sqrt(1-4*2^k*x +x*O(x^n))))^k/k!), n)

Crossrefs

Cf. A136551, A136552.

Sequence in context: A158097 A262003 A271847 * A068369 A034405 A197210

Adjacent sequences: A136547 A136548 A136549 * A136551 A136552 A136553

Keyword

nonn

Author

Paul D. Hanna, Jan 05 2008

Status

approved