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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
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: A151323 A354503 A181662 * A113140 A151324 A121185
KEYWORD
nonn
AUTHOR
Peter Luschny, Apr 24 2014
STATUS
approved