A358957 a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(7*n) * (x^n - 2*A(x))^(8*n+1).

1, 7, 105, 1855, 36225, 753319, 16356809, 366518975, 8412321985, 196761671175, 4672976571753, 112386313863327, 2731613284143345, 66992673654966087, 1655756220596437601, 41199365822954474670, 1031225066096367871764, 25947188077245338061147, 655925022779049206277461

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 + 7*x + 105*x^2 + 1855*x^3 + 36225*x^4 + 753319*x^5 + 16356809*x^6 + 366518975*x^7 + 8412321985*x^8 + 196761671175*x^9 + 4672976571753*x^10 + ...
		

Crossrefs

Cf. A355865, A358952, A358953, A358954, A358955, A358956, A358958, A358959.

Programs

PARI

{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(7*n) * (x^n - 2*Ser(A))^(8*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^(7*n) * (x^n - 2*A(x))^(8*n+1).

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