A275827 a(n) = Sum_{k=0..n} binomial(n+k+2,k)*binomial(2*n+1,n-k).

1, 7, 50, 364, 2688, 20064, 151008, 1144000, 8712704, 66646528, 511673344, 3940579328, 30429184000, 235521884160, 1826663915520, 14192851599360, 110453212446720, 860819570688000, 6717522904350720, 52482715893104640

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

Cf. A000108.

Sequence in context: A054413 A163458 A081571 * A081189 A108869 A065429

Adjacent sequences: A275824 A275825 A275826 * A275828 A275829 A275830

Keyword

nonn

Author

Vladimir Kruchinin, Nov 23 2016

Status

approved