A358959 a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(9*n) * (x^n - 2*A(x))^(10*n+1).

1, 9, 171, 3819, 94221, 2474541, 67842255, 1919233719, 55608288057, 1641837803793, 49218744365683, 1494112796918051, 45836491198618821, 1418839143493455861, 44259772786526485527, 1389967891240928450511, 43910122539568806384513, 1394423517592589134138485

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 + 9*x + 171*x^2 + 3819*x^3 + 94221*x^4 + 2474541*x^5 + 67842255*x^6 + 1919233719*x^7 + 55608288057*x^8 + 1641837803793*x^9 + 49218744365683*x^10 + ...
		

Crossrefs

Cf. A355865, A358952, A358953, A358954, A358955, A358956, A358957, A358958.

Programs

PARI

{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(9*n) * (x^n - 2*Ser(A))^(10*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^(9*n) * (x^n - 2*A(x))^(10*n+1).

(2) 0 = Sum_{n=-oo..+oo} x^(10*n*(n-1)) / (1 - 2*A(x)*x^n)^(10*n-1).