A240997 G.f. satisfies: A(x)^3 = x + A(x*A(x)^2)^2.

1, 1, 2, 21, 340, 7459, 203191, 6563082, 244275977, 10276093457, 481793838446, 24906702642493, 1407549620790557, 86342073783944457, 5714570300215357125, 405973384652872885758, 30817592926484298640320, 2489727584432844543366345, 213310909894977172829098783

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Formula

a(n) ~ c * 2^n * n^(n - 1/3 - log(2/3)/4) / (exp(n) * (log(3/2))^n), where c = 0.253289930600610020471... . - Vaclav Kotesovec, Aug 08 2014

Example

G.f.: A(x) = 1 + x + 2*x^2 + 21*x^3 + 340*x^4 + 7459*x^5 + 203191*x^6 +...
RELATED SERIES.
A(x)^2 = 1 + 2*x + 5*x^2 + 46*x^3 + 726*x^4 + 15682*x^5 + 423101*x^6 +...
A(x*A(x)^2) = 1 + x + 4*x^2 + 34*x^3 + 540*x^4 + 11696*x^5 + 316071*x^6 +...
A(x*A(x)^2)^2 = 1 + 2*x + 9*x^2 + 76*x^3 + 1164*x^4 + 24744*x^5 + 661010*x^6 +...
A(x)^3 = 1 + 3*x + 9*x^2 + 76*x^3 + 1164*x^4 + 24744*x^5 + 661010*x^6 +...

Prog

(PARI) {a(n)=local(A=[1, 1], Ax); for(i=1, n, A=concat(A, 0); Ax=Ser(A);
A[#A]=Vec(1+subst(Ax^2, x, x*Ax^2) - Ax^3)[#A]); A[n+1]}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A240996.

Sequence in context: A189489 A196629 A196637 * A241247 A177234 A099710

Adjacent sequences: A240994 A240995 A240996 * A240998 A240999 A241000

Keyword

nonn

Author

Paul D. Hanna, Aug 06 2014

Status

approved