A156213 - OEIS

%I #2 Mar 30 2012 18:37:16

%S 1,2,26,1756,577190,846763548,5293107304932,138013765804872888,

%T 14838375909837963204230,6530915607537754235471687212,

%U 11710315776946229385945240614099084

%N G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*C(2*n-1,n)*x^n/n ), a power series in x with integer coefficients.

%C Compare to g.f. of Catalan sequence: exp( Sum_{n>=1} C(2*n-1,n)*x^n/n ), where C(2*n-1,n) = A001700(n-1).

%e G.f.: A(x) = 1 + 2*x + 26*x^2 + 1756*x^3 + 577190*x^4 + 846763548*x^5 +...

%e log(A(x)) = 2*x + 2^4*3*x^2/2 + 2^9*10*x^3/3 + 2^16*35*x^4/4 + 2^25*126*x^5/5 +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n,2^(m^2)*binomial(2*m-1,m)*x^m/m)+x*O(x^n)),n)}

%Y Cf. A000108, A001700.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 06 2009