login
A366554
G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^2.
3
1, 1, 0, 0, 1, 2, 1, 0, 2, 6, 6, 2, 5, 20, 30, 20, 19, 70, 140, 140, 112, 266, 630, 840, 762, 1176, 2814, 4620, 5049, 6204, 12936, 24156, 31460, 36894, 63492, 123552, 185471, 228800, 338910, 634920, 1050686, 1411410, 1944800, 3354780, 5820256, 8513804, 11644490
OFFSET
0,6
FORMULA
G.f.: A(x) = 2*(1+x) / (1+sqrt(1-4*x^4*(1+x))).
a(n) = Sum_{k=0..floor(n/4)} binomial(k+1,n-4*k) * binomial(2*k,k)/(k+1).
a(n) = A366589(n) + A366589(n-1).
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(k+1, n-4*k)*binomial(2*k, k)/(k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 13 2023
STATUS
approved