A363103 Expansion of g.f. A(x) satisfying 1/3 = Sum_{n=-oo..+oo} x^n * (2*A(x) + (-x)^n)^(3*n-1).

1, 18, 990, 76437, 6821604, 662170986, 67898785806, 7236062780346, 793535687872488, 88963928271478008, 10150301461460395149, 1174747280984088520626, 137580020162886643530525, 16274396085743934046292733, 1941610878042595564951651347, 233359133706492695158857170850

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..200

Formula

G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following.

(1) 1/3 = Sum_{n=-oo..+oo} x^n * (2*A(x) + (-x)^n)^(3*n-1).

(2) 1/3 = Sum_{n=-oo..+oo} x^(3*n^2) / (1 + 2*A(x)*(-x)^n)^(3*n+1).

Example

G.f.: A(x) = 1 + 18*x + 990*x^2 + 76437*x^3 + 6821604*x^4 + 662170986*x^5 + 67898785806*x^6 + 7236062780346*x^7 + 793535687872488*x^8 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff(-3/2 + sum(m=-#A, #A, x^m * (2*Ser(A) + (-x)^m)^(3*m-1) )*9/2, #A-1); ); A[n+1]}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Sequence in context: A333089 A129009 A042409 * A073960 A095786 A214181

Adjacent sequences: A363100 A363101 A363102 * A363104 A363105 A363106

Keyword

nonn

Author

Paul D. Hanna, May 18 2023

Status

approved