OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} 4^k * binomial(n/2+1/2,k) * binomial(n-1,n-k).
D-finite with recurrence n*(n+1)*(n-2)*a(n) -6*(n-2)*(3*n^2-6*n+1)*a(n-2) -27*n*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Apr 22 2024
Conjecture: a(2n+1) = 2*A371364(). - R. J. Mathar, Apr 22 2024
MAPLE
A372018 := proc(n)
add(4^k*binomial((n+1)/2, k)*binomial(n-1, k-1), k=0..n) ;
%/(n+1) ;
end proc:
seq(A372018(n), n=0..60) ; # R. J. Mathar, Apr 22 2024
PROG
(PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2+1/2, k)*binomial(n-1, n-k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 15 2024
STATUS
approved