OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1108
FORMULA
G.f.: -(sqrt(1-8*x)+3)/(sqrt(1-8*x)*(8*x-2)+16*x-2).
a(n) ~ 3*8^n/sqrt(Pi*n). - Ilya Gutkovskiy, Nov 24 2016
MATHEMATICA
f[n_] := Sum[ Binomial[n + k + 2, k] Binomial[2n + 1, n - k], {k, 0, n}]; Array[f, 21, 0] (* or *)
CoefficientList[ Series[(1 - Sqrt[1 - 8x] - 2 x - 2Sqrt[1 - 8x] x)/(16Sqrt[1 - 8x] x^2), {x, 0, 20}], x] (* Robert G. Wilson v, Nov 23 2016 *)
PROG
(Maxima)
taylor(-(sqrt(1-8*x)+3)/(sqrt(1-8*x)*(8*x-2)+16*x-2), x, 0, 20);
(PARI) x='x+O('x^50); Vec(-(sqrt(1-8*x)+3)/(sqrt(1-8*x)*(8*x-2)+16*x-2)) \\ G. C. Greubel, Apr 10 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Nov 23 2016
STATUS
approved