OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..386
FORMULA
a(n) = [x^n] (1 + n*x)/(1 + 2*(n-2)*x + (n*x)^2)^(3/2).
a(n) = Sum_{k=0..n} (-n+1)^k * (k+1) * binomial(n+1,k+1)^2.
MATHEMATICA
a[n_] := Sum[If[n == n-k == 0, 1, (-n)^(n-k)] * (n+k+1) * Binomial[n, k] * Binomial[n + k, k], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, May 05 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n, (-n)^(n-k)*(n+k+1)*binomial(n, k)*binomial(n+k, k))}
(PARI) {a(n) = polcoef((1+n*x)/(1+2*(n-2)*x+(n*x)^2)^(3/2), n)}
(PARI) {a(n) = sum(k=0, n, (-n+1)^k*(k+1)*binomial(n+1, k+1)^2)}
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jan 19 2020
STATUS
approved