OFFSET
0,2
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.6.3.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n=0..200
M. Kondratiewa and S. Sadov, Markov's transformation of series and the WZ method, arXiv:math/0405592 [math.CA], 2004.
A. J. van der Poorten, A proof that Euler missed ... Apery's proof of the irrationality of zeta(3), Math. Intelligencer 1 (1978/1979), 195-203.
I. J. Zucker, On the series Sum(k>=1) C(2k,k)^(-1)*k^(-n) and related sums, J. Number Theory 20 (1985), no. 1, 92-102.
FORMULA
Sum_{n>=1} (-1)^(n+1) / a(n) = 2 * zeta(3) / 5.
G.f.: (2*x*(2*x*(2*x + 5) + 1))/(1-4*x)^(7/2). - Harvey P. Dale, Apr 08 2012
From Ilya Gutkovskiy, Jan 17 2017: (Start)
a(n) ~ 4^n*n^(5/2)/sqrt(Pi).
Sum_{n>=1} 1/a(n) = (1/2)*4F3(1,1,1,1; 3/2,2,2; 1/4) = A145438. (End)
MATHEMATICA
Table[n^3 Binomial[2n, n], {n, 0, 30}] (* Harvey P. Dale, Apr 08 2012 *)
CoefficientList[Series[(2*x*(2*x*(2*x+5)+1))/(1-4*x)^(7/2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2014 *)
PROG
(Magma) [Binomial(2*n, n)*n^3 : n in [0..30]]; // Wesley Ivan Hurt, Oct 21 2014
(SageMath) [n^3*binomial(2*n, n) for n in range(31)] # G. C. Greubel, Nov 19 2022
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
Entry revised by N. J. A. Sloane, Apr 06 2004
STATUS
approved