A358953 a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(3*n) * (x^n - 2*A(x))^(4*n+1).

1, 3, 21, 159, 1369, 12131, 111489, 1042310, 9878188, 94345595, 905236045, 8698907855, 83509981377, 798911473287, 7596665295846, 71585365842419, 666055801137389, 6089025714101416, 54304588402962717, 467144137463862047, 3798557443794080777, 27983895459969702990

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..21.

Formula

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

(1) 0 = Sum_{n=-oo..+oo} x^(3*n) * (x^n - 2*A(x))^(4*n+1).

(2) 0 = Sum_{n=-oo..+oo} x^(4*n*(n-1)) / (1 - 2*A(x)*x^n)^(4*n-1).

Example

G.f.: A(x) = 1 + 3*x + 21*x^2 + 159*x^3 + 1369*x^4 + 12131*x^5 + 111489*x^6 + 1042310*x^7 + 9878188*x^8 + 94345595*x^9 + 905236045*x^10 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(n=-#A, #A, x^(3*n) * (x^n - 2*Ser(A))^(4*n+1) ), #A-1)/2); A[n+1]}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A355865, A358952, A358954, A358955, A358956, A358957, A358958, A358959.

Sequence in context: A192364 A286918 A372463 * A189508 A074570 A136781

Adjacent sequences: A358950 A358951 A358952 * A358954 A358955 A358956

Keyword

nonn

Author

Paul D. Hanna, Dec 07 2022

Status

approved