cp's OEIS Frontend

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.

A160222 Numerator of Hermite(n, 25/28).

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%I A160222 #11 Sep 08 2022 08:45:45
%S A160222 1,25,233,-13775,-618383,6139625,1365521305,19697634625,
%T A160222 -3254549595295,-143135522066375,7903662920541385,758682819513724625,
%U A160222 -15113524025531336495,-3946682083630844048375,-21648533656663410430855,21118177933549486876710625
%N A160222 Numerator of Hermite(n, 25/28).
%H A160222 G. C. Greubel, <a href="/A160222/b160222.txt">Table of n, a(n) for n = 0..417</a>
%F A160222 From _G. C. Greubel_, Sep 26 2018: (Start)
%F A160222 a(n) = 14^n * Hermite(n, 25/28).
%F A160222 E.g.f.: exp(25*x - 196*x^2).
%F A160222 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(25/14)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160222 Numerators of 1, 25/14, 233/196, -13775/2744, -618383/38416
%t A160222 Table[14^n*HermiteH[n, 25/28], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)
%o A160222 (PARI) a(n)=numerator(polhermite(n, 25/28)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160222 (PARI) x='x+O('x^30); Vec(serlaplace(exp(25*x - 196*x^2))) \\ _G. C. Greubel_, Sep 26 2018
%o A160222 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(25/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018
%Y A160222 Cf. A001023 (denominators).
%K A160222 sign,frac
%O A160222 0,2
%A A160222 _N. J. A. Sloane_, Nov 12 2009