A241524 a(n) = 4^n*(n/4 + binomial(n+1/2, 1/2)).

1, 7, 38, 188, 886, 4052, 18156, 80152, 349862, 1513604, 6501316, 27759272, 117935548, 498920008, 2102905496, 8835174960, 37015522054, 154690661732, 645017651412, 2684135346184, 11149265820500, 46234832784216, 191441476611688, 791591523218768, 3268982440735836

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi)

Formula

a(n) = 4^n*(n/4 + 2*Gamma(n+3/2)/(sqrt(Pi)*Gamma(n+1))).

G.f.: (x + sqrt(1 - 4*x))/(1 - 4*x)^2. - Ilya Gutkovskiy, Feb 15 2017

Maple

seq(4^n*(n/4 + binomial(n+1/2, 1/2)), n=0..24);

Mathematica

Table[4^n (n/4 + Binomial[n + 1/2, 1/2]), {n, 0, 40}] (* Vincenzo Librandi, Apr 25 2014 *)

Prog

(PARI) for(n=0, 25, print1(round(4^n*(n/4 + 2*gamma(n+3/2)/(sqrt(Pi)*gamma(n+1)))), ", ")) \\ G. C. Greubel, Feb 14 2017

Crossrefs

Cf. A241478.

Sequence in context: A277912 A000531 A296769 * A291822 A099453 A292535

Adjacent sequences: A241521 A241522 A241523 * A241525 A241526 A241527

Keyword

nonn

Author

Peter Luschny, Apr 24 2014

Status

approved