A120605 G.f. satisfies: 25*A(x) = 24 + 64*x + A(x)^9, starting with [1,4,36].

1, 4, 36, 984, 31716, 1140552, 43895208, 1768717872, 73674176868, 3146885203432, 137085166193976, 6066992348458704, 272023207778276136, 12330039492509279184, 564072488005316830416, 26010805156782400648800

Offset

0,2

Comments

See comments in A120588 for conditions needed for an integer sequence to satisfy a functional equation of the form: r*A(x) = c + b*x + A(x)^n.

Links

Table of n, a(n) for n=0..15.

Formula

G.f.: A(x) = 1 + Series_Reversion((1+25*x - (1+x)^9)/64). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(9*n,n)/(8*n+1) * (24+64*x)^(8*n+1)/25^(9*n+1). - Paul D. Hanna, Jan 24 2008

a(n) ~ 4^(-1 + 3*n) * (-24 + 8*(5/3)^(9/4))^(1/2 - n) / (3^(1/8) * 5^(7/8) * n^(3/2) * sqrt(Pi)). - Vaclav Kotesovec, Nov 28 2017

Example

A(x) = 1 + 4*x + 36*x^2 + 984*x^3 + 31716*x^4 + 1140552*x^5 +...
A(x)^9 = 1 + 36*x + 900*x^2 + 24600*x^3 + 792900*x^4 + 28513800*x^5 +...

Mathematica

CoefficientList[1 + InverseSeries[Series[(1+25*x - (1+x)^9)/64, {x, 0, 20}], x], x] (* Vaclav Kotesovec, Nov 28 2017 *)

Prog

(PARI) {a(n)=local(A=1+4*x+36*x^2+x*O(x^n)); for(i=0, n, A=A+(-25*A+24+64*x+A^9)/16); polcoeff(A, n)}

Crossrefs

Cf. A120588 - A120604, A120606, A120607.

Sequence in context: A127901 A061742 A136469 * A337851 A353410 A360725

Adjacent sequences: A120602 A120603 A120604 * A120606 A120607 A120608

Keyword

nonn

Author

Paul D. Hanna, Jun 16 2006

Status

approved