A128418 a(n) = Sum_{k=0..n} 2^(n-k)*C(2n,n-k).

1, 5, 33, 233, 1697, 12585, 94449, 714873, 5445441, 41687369, 320420753, 2471008281, 19108837601, 148123058153, 1150532419377, 8952614975673, 69772391628417, 544532315255433, 4255064364533457, 33287174505889113, 260669265451935777, 2043172307192457513, 16028314647309873777

Offset

0,2

Comments

Row sums of number triangle A128417.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: 8*x/(sqrt(1-8*x)*(sqrt(1-8*x)+12*x-1));

Conjecture: n^2*a(n)+(12+4*n-17*n^2)*a(n-1) +36*(n+1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Nov 05 2012

a(n) ~ 2^(3*n+1) / sqrt(Pi*n). - Vaclav Kotesovec, Feb 03 2014

Mathematica

Table[Sum[2^(n-k) Binomial[2n, n-k], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Jan 06 2013 *)

Prog

(PARI) x='x +O('x^50); Vec(8*x/(sqrt(1-8*x)*(sqrt(1-8*x)+12*x-1))) \\ G. C. Greubel, Feb 09 2017

Crossrefs

Sequence in context: A083076 A361237 A162816 * A335119 A284733 A001887

Adjacent sequences: A128415 A128416 A128417 * A128419 A128420 A128421

Keyword

easy,nonn

Author

Paul Barry, Mar 02 2007

Status

approved