A358958 a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(8*n) * (x^n - 2*A(x))^(9*n+1).

1, 8, 136, 2720, 60112, 1414400, 34744192, 880722944, 22866372480, 604987038208, 16252230833792, 442118711113216, 12154717695451712, 337169716435693120, 9425612400257630864, 265272780558100130464, 7510038750103097772890, 213729057394800722424678, 6110972702751703321123745

Offset: 0

Author

Paul D. Hanna, Dec 07 2022

Keywords

• nonn

Comments

Related identity: 0 = Sum_{n=-oo..+oo} x^n * (y - x^n)^n, which holds formally for all y.

Examples

			G.f.: A(x) = 1 + 8*x + 136*x^2 + 2720*x^3 + 60112*x^4 + 1414400*x^5 + 34744192*x^6 + 880722944*x^7 + 22866372480*x^8 + 604987038208*x^9 + 16252230833792*x^10 + ...
		

Crossrefs

Cf. A355865, A358952, A358953, A358954, A358955, A358956, A358957, A358959.

Programs

PARI

{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(8*n) * (x^n - 2*Ser(A))^(9*n+1) ), #A-1)/2);A[n+1]}
for(n=0,25,print1(a(n),", "))

Formula

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

(1) 0 = Sum_{n=-oo..+oo} x^(8*n) * (x^n - 2*A(x))^(9*n+1).

(2) 0 = Sum_{n=-oo..+oo} x^(9*n*(n-1)) / (1 - 2*A(x)*x^n)^(9*n-1).