OFFSET
0,3
FORMULA
a(n) = [x^n] 2/(1 + x + sqrt(1 - x*(2 + 4*n - x))).
a(n) = Sum_{k=0..n} (-1)^(n-k)*(n + 1)^k*binomial(n,k)*binomial(n+k,k)/(k + 1).
a(n) ~ exp(1/2) * 2^(2*n) * n^(n - 3/2) / sqrt(Pi). - Vaclav Kotesovec, Jun 08 2019
MATHEMATICA
Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-n x, 1 - x, {i, 1, n}]), {x, 0, n}], {n, 0, 17}]
Table[SeriesCoefficient[2/(1 + x + Sqrt[1 - x (2 + 4 n - x)]), {x, 0, n}], {n, 0, 17}]
Table[Sum[(-1)^(n - k) (n + 1)^k Binomial[n, k] Binomial[n + k, k]/(k + 1), {k, 0, n}], {n, 0, 17}]
Table[(-1)^n Hypergeometric2F1[-n, n + 1, 2, n + 1], {n, 0, 17}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 21 2018
STATUS
approved