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 A002423 M4934 N2114 #51 Mar 24 2022 08:05:10
%S A002423 1,-14,70,-140,70,28,28,40,70,140,308,728,1820,4760,12920,36176,
%T A002423 104006,305900,917700,2801400,8684340,27293640,86843400,279409200,
%U A002423 908079900,2978502072,9851968392,32839894640
%N A002423 Expansion of (1-4*x)^(7/2).
%D A002423 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 A002423 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002423 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A002423 T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 164.
%H A002423 Vincenzo Librandi, <a href="/A002423/b002423.txt">Table of n, a(n) for n = 0..1000</a>
%H A002423 N. J. A. Sloane, <a href="/A000984/a000984.pdf">Notes on A984 and A2420-A2424</a>
%F A002423 a(n) = Sum_{m=0..n} binomial(n, m) * K_m(8), where K_m(x) = K_m(n, 2, x) is a Krawtchouk polynomial. - Alexander Barg (abarg(AT)research.bell-labs.com)
%F A002423 a(n) ~ 105*4^(n-2)/(sqrt(Pi)*n^(9/2)). - _Vaclav Kotesovec_, Jul 28 2013
%F A002423 a(n) = (105/16)*4^n*Gamma(-7/2+n)/(sqrt(Pi)*Gamma(1+n)). - _Peter Luschny_, Dec 14 2015
%F A002423 a(n) = (-4)^n * binomial(7/2, n). - _G. C. Greubel_, Jul 03 2019
%F A002423 D-finite with recurrence: n*a(n) +2*(-2*n+9)*a(n-1)=0. - _R. J. Mathar_, Jan 16 2020
%F A002423 From _Amiram Eldar_, Mar 24 2022: (Start)
%F A002423 Sum_{n>=0} 1/a(n) = 36/35 + 2*Pi/(3^4*sqrt(3)).
%F A002423 Sum_{n>=0} (-1)^n/a(n) = 23932/21875 - 36*log(phi)/(5^5*sqrt(5)), where phi is the golden ratio (A001622). (End)
%p A002423 A002423 := n -> (105/16)*4^n*GAMMA(-7/2+n)/(sqrt(Pi)*GAMMA(1+n)):
%p A002423 seq(A002423(n), n=0..27); # _Peter Luschny_, Dec 14 2015
%t A002423 CoefficientList[Series[(1-4*x)^(7/2),{x,0,30}],x] (* _Jean-François Alcover_, Mar 21 2011 *)
%t A002423 Table[(4^(-1+x) Pochhammer[-(7/2),-1+x])/Pochhammer[1,-1+x],{x,30}] (* _Harvey P. Dale_, Jul 13 2011 *)
%o A002423 (PARI) vector(30, n, n--; (-4)^n*binomial(7/2, n)) \\ _G. C. Greubel_, Jul 03 2019
%o A002423 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-4*x)^(7/2) )); // _G. C. Greubel_, Jul 03 2019
%o A002423 (Sage) [(-4)^n*binomial(7/2, n) for n in (0..30)] # _G. C. Greubel_, Jul 03 2019
%Y A002423 Cf. A007054, A004001, A002420, A002421, A002422, A002424, A007272, A001622.
%K A002423 sign,easy,nice
%O A002423 0,2
%A A002423 _N. J. A. Sloane_