A120916 G.f. satisfies: A(x) = C(2x)*A(x^3*C(2x)^4), where C(x) is the g.f. of the Catalan numbers (A000108).

1, 2, 8, 42, 244, 1504, 9656, 63856, 431872, 2972778, 20756036, 146627648, 1046060836, 7525452296, 54530660832, 397628393728, 2915496099136, 21481907631872, 158975372309176, 1181109256858096, 8806197969093184

Offset: 0

Author

Paul D. Hanna, Jul 17 2006

Keywords

• nonn

Comments

Self-convolution equals A120915, which equals column 0 of triangle A120914 (cascadence of (1+2x)^2).

Crossrefs

Cf. A120914, A120915, A000108.

Programs

PARI

{a(n)=local(A=1+2*x,C=(1/x*serreverse(x/(1+4*x+4*x^2+x*O(x^n))))^(1/2)); for(i=0,n,A=C*subst(A,x,x^3*C^4 +x*O(x^n)));polcoeff(A,n,x)}