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
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi)
N. J. A. Sloane, Notes on A984 and A2420-A2424
FORMULA
a(n+3) = -2 * A007272(n).
a(n) = Sum_{m=0..n} binomial(n, m) * K_m(6), where K_m(x) = K_m(n, 2, x) is a Krawtchouk polynomial. - Alexander Barg (abarg(AT)research.bell-labs.com).
a(n) ~ -15/8*Pi^(-1/2)*n^(-7/2)*2^(2*n)*{1 + 35/8*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 22 2001
a(n) = -(15/8)*4^n*Gamma(n-5/2)/(sqrt(Pi)*Gamma(1+n)). - Peter Luschny, Dec 14 2015
a(n) = (-4)^n*binomial(5/2, n). - Peter Luschny, Oct 22 2018
D-finite with recurrence: n*a(n) +2*(-2*n+7)*a(n-1)=0. - R. J. Mathar, Jan 16 2020
From Amiram Eldar, Mar 24 2022: (Start)
Sum_{n>=0} 1/a(n) = 32/45 - 14*Pi/(3^5*sqrt(3)).
Sum_{n>=0} (-1)^n/a(n) = 2144/1875 - 28*log(phi)/(5^4*sqrt(5)), where phi is the golden ratio (A001622). (End)
MAPLE
A002422 := n -> -(15/8)*4^n*GAMMA(n-5/2)/(sqrt(Pi)*GAMMA(1+n)):
seq(A002422(n), n=0..26); # Peter Luschny, Dec 14 2015
MATHEMATICA
CoefficientList[Series[(1-4x)^{5/2}, {x, 0, 30}], x] (* Vincenzo Librandi, Jun 11 2012 *)
PROG
(PARI) vector(30, n, n--; (-4)^n*binomial(5/2, n)) \\ G. C. Greubel, Jul 03 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-4*x)^(5/2) )); // G. C. Greubel, Jul 03 2019
(Sage) [(-4)^n*binomial(5/2, n) for n in (0..30)] # G. C. Greubel, Jul 03 2019
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved