OFFSET
0,2
FORMULA
a(n) = Sum_{k = 0..n} binomial(n+k, n-k)/(2*k+1) * (2*n+1)^k
a(n)^2 = 2/(2*n + 1)^3 * (T(2*n+1, n+3/2) - 1), where T(n, x) denotes the n-th Chebyshev polynomial of the first kind.
MAPLE
seq(add(binomial(n+k, n-k)/(2*k+1) * (2*n+1)^k, k = 0..n), n = 0..20);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Apr 03 2024
STATUS
approved