OFFSET
0,2
REFERENCES
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 55.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 164.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Alexander Barg, Stolarsky's invariance principle for finite metric spaces, arXiv:2005.12995 [math.CO], 2020.
N. J. A. Sloane, Notes on A984 and A2420-A2424.
FORMULA
a(n) = Sum_{m=0..n} binomial(n, m) * K_m(10), where K_m(x) = K_m(n, 2, x) is a Krawtchouk polynomial. - Alexander Barg, abarg(AT)research.bell-labs.com.
a(n) = -(945/32)*4^n*Gamma(-9/2+n)/(sqrt(Pi)*Gamma(1+n)). - Peter Luschny, Dec 14 2015
a(n) = (-4)^n*binomial(9/2, n). - G. C. Greubel, Jul 03 2019
D-finite with recurrence: n*a(n) +2*(-2*n+11)*a(n-1)=0. - R. J. Mathar, Jan 16 2020
From Amiram Eldar, Mar 25 2022: (Start)
Sum_{n>=0} 1/a(n) = 32/35 - 22*Pi/(3^7*sqrt(3)).
Sum_{n>=0} (-1)^n/a(n) = 1050752/984375 - 44*log(phi)/(5^6*sqrt(5)), where phi is the golden ratio (A001622). (End)
MAPLE
A002424 := n -> -(945/32)*4^n*GAMMA(-9/2+n)/(sqrt(Pi)*GAMMA(1+n)):
seq(A002424(n), n=0..28); # Peter Luschny, Dec 14 2015
MATHEMATICA
CoefficientList[Series[(1-4x)^(9/2), {x, 0, 30}], x] (* Harvey P. Dale, Dec 27 2011 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1-4*x)^(9/2)) \\ Altug Alkan, Dec 14 2015
(PARI) vector(30, n, n--; (-4)^n*binomial(9/2, n)) \\ G. C. Greubel, Jul 03 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-4*x)^(9/2) )); // G. C. Greubel, Jul 03 2019
(Sage) [(-4)^n*binomial(9/2, n) for n in (0..30)] # G. C. Greubel, Jul 03 2019
CROSSREFS
KEYWORD
sign,easy,nice
AUTHOR
STATUS
approved