A358956 a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(6*n) * (x^n - 2*A(x))^(7*n+1).

1, 6, 78, 1196, 20280, 366288, 6908744, 134492752, 2681961056, 54504790720, 1124768357872, 23505633975616, 496452504891320, 10580216111991080, 227237269499825185, 4913552644294206262, 106877300690757456293, 2336971970184440328572, 51339570414117180476064

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 + 6*x + 78*x^2 + 1196*x^3 + 20280*x^4 + 366288*x^5 + 6908744*x^6 + 134492752*x^7 + 2681961056*x^8 + 54504790720*x^9 + 1124768357872*x^10 + ...
		

Crossrefs

Cf. A355865, A358952, A358953, A358954, A358955, 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^(6*n) * (x^n - 2*Ser(A))^(7*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^(6*n) * (x^n - 2*A(x))^(7*n+1).

(2) 0 = Sum_{n=-oo..+oo} x^(7*n*(n-1)) / (1 - 2*A(x)*x^n)^(7*n-1).