A128326 G.f.: A(x) = 1 + G(G(G(x))), where G(x) = x + x*G(G(x)) is the g.f. of A030266.

1, 1, 3, 12, 57, 305, 1787, 11269, 75629, 535960, 3987913, 31021693, 251445581, 2117993712, 18499513147, 167246537937, 1562556275281, 15066167302802, 149737897716757, 1532313152898208, 16129331500727047

Offset

0,3

Comments

Equals row 1 of table A128325.

Links

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

Formula

G.f. satisfies: A(x) = x/(1 - A( x/(1 - A(x)) )) when offset is taken to be 1. - Paul D. Hanna, Dec 20 2014

Prog

(PARI) {a(n)=local(A=1+x, B); for(i=0, n, A = 1 + x*A * subst(A, x, x*A+x*O(x^n))); B=A; B=subst(B, x, x*A+x*O(x^n)); polcoeff(B, n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A = 1/subst(1-x*A, x, x/(1-x*A +x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A030266; A128325 (table), A128327 (row 2), A128328 (row 3), A128329 (main diagonal).

Sequence in context: A291695 A117107 A159609 * A323631 A014333 A185618

Adjacent sequences: A128323 A128324 A128325 * A128327 A128328 A128329

Keyword

nonn

Author

Paul D. Hanna, Mar 11 2007

Status

approved