A145158 G.f. A(x) satisfies A(x/A(x)^2) = 1/(1-x).

1, 1, 3, 16, 121, 1143, 12570, 154551, 2072547, 29829412, 455731327, 7332989616, 123548350018, 2169987439342, 39595583375433, 748541216196285, 14628467191450947, 294984129900772611, 6128372452917891216

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..160

Formula

G.f. satisfies: 1 - 1/A(x) = x*A( 1 - 1/A(x) )^2.

Self-convolution yields A145159.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 121*x^4 + 1143*x^5 +...
x/A(x)^2 = x - 2*x^2 - 3*x^3 - 18*x^4 - 150*x^5 - 1518*x^6 -...
1/A(x) = 1 - x - 2*x^2 - 11*x^3 - 88*x^4 - 869*x^5 - 9876*x^6 -...
Series_Reversion[x/A(x)^2] = x + 2*x^2 + 11*x^3 + 88*x^4 + 869*x^5 +...

Prog

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

Crossrefs

Cf. A145161 (A^3); A088713, A145160, A145162, A145165, A145167.

Sequence in context: A120015 A003692 A166883 * A132070 A362204 A121629

Adjacent sequences: A145155 A145156 A145157 * A145159 A145160 A145161

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2008

Status

approved