OFFSET
0,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..300
FORMULA
G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following.
(1) 2 = Sum_{n=-oo..+oo} (-1)^n * x^n * (A(x) + x^(2*n))^(2*n+1).
(2) 2 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(4*n-3)) / (1 + A(x)*x^(2*n))^(2*n-1).
EXAMPLE
G.f.: A(x) = 1 + 2*x + 5*x^2 + 20*x^3 + 86*x^4 + 396*x^5 + 1887*x^6 + 9277*x^7 + 46748*x^8 + 240189*x^9 + 1253474*x^10 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff(2 - sum(m=-#A, #A, (-1)^m * x^m * (Ser(A) + x^(2*m))^(2*m+1) ), #A-1)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 17 2023
STATUS
approved