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

0,2

Comments

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

Links

Table of n, a(n) for n=0..20.

Prog

(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)}

Crossrefs

Cf. A120914, A120915, A000108.

Sequence in context: A366238 A357402 A129277 * A133417 A235350 A100327

Adjacent sequences: A120913 A120914 A120915 * A120917 A120918 A120919

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2006

Status

approved