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A361774
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(4*n-1).
4
1, 4, 150, 7003, 380817, 22517717, 1405927141, 91215539609, 6089092570148, 415519886498886, 28855638743197866, 2032628861705203315, 144884697917577076857, 10430845410431559928714, 757390467820895322043476, 55401570124877193188443429, 4078685155312165112343519832
OFFSET
0,2
FORMULA
G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.
(1) 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(4*n-1).
(2) 1 = Sum_{n=-oo..+oo} (-1)^(n+1) * x^(4*n^2) / (1 - 2*A(x)*(-x)^n)^(4*n+1).
EXAMPLE
G.f.: A(x) = 1 + 4*x + 150*x^2 + 7003*x^3 + 380817*x^4 + 22517717*x^5 + 1405927141*x^6 + 91215539609*x^7 + 6089092570148*x^8 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=-#A, #A, x^m * (2*Ser(A) - (-x)^m)^(4*m-1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 13 2023
STATUS
approved