A136551 a(n) = C(2^n + 2*n + 1, n)*(2^n + 1)/(2^n + 2*n + 1); a(n) = coefficient of x^n in Catalan(x)^(2^n+1).

1, 3, 20, 273, 8602, 738738, 200144100, 188542438797, 649522995031926, 8346577591515964350, 402021093245772461553820, 72549434962879252821217976994, 48999971145855741423248927935058060

Offset

0,2

Links

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

Formula

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

Example

G.f.: A(x) = 1 + 3*x + 20*x^2 + 273*x^3 + 8602*x^4 + 738738*x^5 +...

Prog

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

Crossrefs

Cf. A136550, A136552.

Sequence in context: A193194 A320945 A166232 * A266812 A086229 A369322

Adjacent sequences: A136548 A136549 A136550 * A136552 A136553 A136554

Keyword

nonn

Author

Paul D. Hanna, Jan 05 2008

Status

approved