A125279 G.f.: A(x) = (1/x)*series_reversion(x^2/G(x)) where G(x) is the g.f. of A030266, which shifts left under self-COMPOSE.

1, 1, 3, 13, 68, 400, 2555, 17375, 124280, 927711, 7189102, 57627044, 476645965, 4061184195, 35604795538, 320957712849, 2973550524004, 28305757130713, 276806230525768, 2780528226936569, 28686373905833717, 303913110837114965

Offset

0,3

Comments

Derived from central terms of triangle: a(n) = A125278(2*n,n)/(n+1).

Links

Table of n, a(n) for n=0..21.

Formula

G.f. satisfies: A(x) = 1 + x*A(x)^2 * A( x^2*A(x)^4/(A(x) - 1) ). By definition, G.f. satisfies: A(x) = 1 + G(x*A(x)^2); G(x*A(x)) = x*A(x)^2; x*A(x^2/G(x)) = G(x); where G(x) = x + x*G(G(x)) is g.f. of A030266.

Example

A(x) = 1 + x + 3*x^2 + 13*x^3 + 68*x^4 + 400*x^5 + 2555*x^6 +...
The g.f. of A030266 is G(x) = x + x*G(G(x)) where
G(x) = x + x^2 + 2*x^3 + 6*x^4 + 23*x^5 + 104*x^6 + 531*x^7 + 2982*x^8+..

Prog

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

Crossrefs

Cf. A030266, A125278.

Sequence in context: A200757 A000260 A192737 * A186371 A121954 A058307

Adjacent sequences: A125276 A125277 A125278 * A125280 A125281 A125282

Keyword

nonn

Author

Paul D. Hanna, Nov 26 2006

Status

approved