A358955 a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(5*n) * (x^n - 2*A(x))^(6*n+1).

1, 5, 55, 715, 10285, 157577, 2521339, 41635879, 704264465, 12139738505, 212475103777, 3765897874074, 67454279084444, 1219122315546851, 22204489538545069, 407150017658467685, 7509869807043464691, 139245172845883281403, 2593887890033997265241, 48521833007161546858193

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 + 5*x + 55*x^2 + 715*x^3 + 10285*x^4 + 157577*x^5 + 2521339*x^6 + 41635879*x^7 + 704264465*x^8 + 12139738505*x^9 + 212475103777*x^10 + ...
		

Crossrefs

Cf. A355865, A358952, A358953, A358954, A358956, A358957, 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^(5*n) * (x^n - 2*Ser(A))^(6*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^(5*n) * (x^n - 2*A(x))^(6*n+1).

(2) 0 = Sum_{n=-oo..+oo} x^(6*n*(n-1)) / (1 - 2*A(x)*x^n)^(6*n-1).