OFFSET
0,2
COMMENTS
Compare to A355865.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..300
FORMULA
Generating function A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
(1) 2 = Sum_{n=-oo..+oo} (-1)^n * x^n * (2*A(x) + x^n)^(2*n+1).
(2) 2 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n*(n-1)) / (1 + 2*A(x)*x^n)^(2*n-1).
EXAMPLE
G.f.: A(x) = 1 + 3*x + 25*x^2 + 254*x^3 + 2763*x^4 + 32180*x^5 + 393169*x^6 + 4964017*x^7 + 64254694*x^8 + 848214039*x^9 + 11375359344*x^10 + ...
PROG
(PARI) {a(n) = my(A=1); for(L=1, n, A = truncate(A);
A = A + 1 - (1/2)*sum(m=-L, L, (-1)^m * x^m * (2*A + x^m +x^2*O(x^(L+1)))^(2*m+1) ) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 14 2022
STATUS
approved