A156213 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.

1, 2, 26, 1756, 577190, 846763548, 5293107304932, 138013765804872888, 14838375909837963204230, 6530915607537754235471687212, 11710315776946229385945240614099084

Offset: 0

Author

Paul D. Hanna, Feb 06 2009

Keywords

• nonn

Comments

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).

Examples

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

Crossrefs

Cf. A000108, A001700.

Programs

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)}