A120915 G.f. satisfies: A(x) = C(2x)^2 * A(x^3*C(2x)^4), where C(x) is the g.f. of the Catalan numbers (A000108).

1, 4, 20, 116, 720, 4656, 30996, 210896, 1459536, 10239796, 72651184, 520328112, 3756512912, 27307671040, 199705789248, 1468209751856, 10844681408064, 80437588353600, 598867568439828, 4473784063109904, 33524058847464912

Offset

0,2

Comments

Column 0 of triangle A120914 (cascadence of (1+2x)^2).

Links

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

Example

A(x) = 1 + 4*x + 20*x^2 + 116*x^3 + 720*x^4 + 4656*x^5 + 30996*x^6 +...
= C(2x)^2 * A(x^3*C(2x)^4) where
C(2x) = 1 + 2*x + 8*x^2 + 40*x^3 + 224*x^4 + 1344*x^5 + 8448*x^6 +...
and C(x) is g.f. of the Catalan numbers (A000108): C(x) = 1 + x*C(x)^2.

Prog

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

Crossrefs

Cf. A120914, A120916 (square-root), A120917, A120918; A000108; variants: A092684, A092687, A120895, A120899, A120920.

Sequence in context: A077445 A085458 A085456 * A165311 A367283 A363556

Adjacent sequences: A120912 A120913 A120914 * A120916 A120917 A120918

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2006

Status

approved