OFFSET
0,2
FORMULA
G.f.: A(x) = (1+4*x)/(-2*x^2 + sqrt(1+4*x+4*x^4)).
a(n) = Sum_{k=0..n} 4^k * binomial(n/2-k/2+1/2,k) * binomial(k,n-k)/(n-k+1).
D-finite with recurrence n*a(n) +2*(2*n-3)*a(n-1) +4*(n-6)*a(n-4)=0. - R. J. Mathar, Apr 22 2024
MAPLE
A372002 := proc(n)
add(4^k*binomial((n-k+1)/2, k)*binomial(k, n-k)/(n-k+1), k=0..n) ;
end proc:
seq(A372002(n), n=0..60) ; # R. J. Mathar, Apr 22 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec((1+4*x)/(-2*x^2+sqrt(1+4*x+4*x^4)))
(PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2-k/2+1/2, k)*binomial(k, n-k)/(n-k+1));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 15 2024
STATUS
approved