A136551 - OEIS

%I #4 Jun 13 2015 10:23:10

%S 1,3,20,273,8602,738738,200144100,188542438797,649522995031926,

%T 8346577591515964350,402021093245772461553820,

%U 72549434962879252821217976994,48999971145855741423248927935058060

%N 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).

%F 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)).

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

%o (PARI) a(n)=binomial(2^n + 2*n + 1, n)*(2^n + 1)/(2^n + 2*n + 1)

%o (PARI) a(n)=polcoeff((2/(1+sqrt(1-4*x +x*O(x^n))))^(2^n+1),n)

%o (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)

%Y Cf. A136550, A136552.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 05 2008