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A241478 a(n) = 4^n*(n/4 + binomial(n-1/2, -1/2)). 2
1, 3, 14, 68, 326, 1532, 7068, 32104, 143942, 638444, 2806196, 12239768, 53035804, 228504408, 979640696, 4181649360, 17780949574, 75348050252, 318312780612, 1341015321784, 5635404667700, 23628002057736, 98861122208008, 412853709749168, 1721097463947036 (list; graph; refs; listen; history; text; internal format)
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 + Gamma(n+1/2)/(sqrt(Pi)*Gamma(n+1))).

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

MAPLE

A241478 := n -> 4^n*(n/4+GAMMA(n+1/2)/(sqrt(Pi)*GAMMA(n+1))); seq(A241478(n), 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 + gamma(n+1/2)/(sqrt(Pi)*gamma(n+1)))), ", ")) \\ G. C. Greubel, Feb 14 2017

CROSSREFS

Cf. A241524.

Sequence in context: A002320 A151323 A181662 * A113140 A151324 A121185

Adjacent sequences:  A241475 A241476 A241477 * A241479 A241480 A241481

KEYWORD

nonn

AUTHOR

Peter Luschny, Apr 24 2014

STATUS

approved

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Last modified September 19 11:18 EDT 2021. Contains 347556 sequences. (Running on oeis4.)