This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002422 M4692 N2003 #51 Mar 24 2022 08:05:04
%S A002422 1,-10,30,-20,-10,-12,-20,-40,-90,-220,-572,-1560,-4420,-12920,-38760,
%T A002422 -118864,-371450,-1179900,-3801900,-12406200,-40940460,-136468200,
%U A002422 -459029400,-1556708400,-5318753700,-18296512728,-63334082520
%N A002422 Expansion of (1-4*x)^(5/2).
%D A002422 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.
%D A002422 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002422 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A002422 T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 164.
%H A002422 G. C. Greubel, <a href="/A002422/b002422.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..100 from Vincenzo Librandi)
%H A002422 N. J. A. Sloane, <a href="/A000984/a000984.pdf">Notes on A984 and A2420-A2424</a>
%F A002422 a(n+3) = -2 * A007272(n).
%F A002422 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).
%F A002422 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
%F A002422 a(n) = -(15/8)*4^n*Gamma(n-5/2)/(sqrt(Pi)*Gamma(1+n)). - _Peter Luschny_, Dec 14 2015
%F A002422 a(n) = (-4)^n*binomial(5/2, n). - _Peter Luschny_, Oct 22 2018
%F A002422 D-finite with recurrence: n*a(n) +2*(-2*n+7)*a(n-1)=0. - _R. J. Mathar_, Jan 16 2020
%F A002422 From _Amiram Eldar_, Mar 24 2022: (Start)
%F A002422 Sum_{n>=0} 1/a(n) = 32/45 - 14*Pi/(3^5*sqrt(3)).
%F A002422 Sum_{n>=0} (-1)^n/a(n) = 2144/1875 - 28*log(phi)/(5^4*sqrt(5)), where phi is the golden ratio (A001622). (End)
%p A002422 A002422 := n -> -(15/8)*4^n*GAMMA(n-5/2)/(sqrt(Pi)*GAMMA(1+n)):
%p A002422 seq(A002422(n), n=0..26); # _Peter Luschny_, Dec 14 2015
%t A002422 CoefficientList[Series[(1-4x)^{5/2},{x,0,30}],x] (* _Vincenzo Librandi_, Jun 11 2012 *)
%o A002422 (PARI) vector(30, n, n--; (-4)^n*binomial(5/2, n)) \\ _G. C. Greubel_, Jul 03 2019
%o A002422 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-4*x)^(5/2) )); // _G. C. Greubel_, Jul 03 2019
%o A002422 (Sage) [(-4)^n*binomial(5/2, n) for n in (0..30)] # _G. C. Greubel_, Jul 03 2019
%Y A002422 Cf. A007054, A004001, A002420, A002421, A002423, A002424, A007272, A001622.
%K A002422 sign
%O A002422 0,2
%A A002422 _N. J. A. Sloane_