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.

A160298 Numerator of Hermite(n, 29/30).

This page as a plain text file.
%I A160298 #13 Sep 08 2022 08:45:45
%S A160298 1,29,391,-14761,-955919,-1151851,2117414071,64515005759,
%T A160298 -4798919156639,-371422676274931,8664364972414951,1922668627437223079,
%U A160298 12868783582225461841,-10009215864276466233211,-365549644020036472532969,52457120268360679565773199
%N A160298 Numerator of Hermite(n, 29/30).
%H A160298 G. C. Greubel, <a href="/A160298/b160298.txt">Table of n, a(n) for n = 0..412</a>
%F A160298 From _G. C. Greubel_, Oct 04 2018: (Start)
%F A160298 a(n) = 15^n * Hermite(n, 29/30).
%F A160298 E.g.f.: exp(29*x - 225*x^2).
%F A160298 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(29/15)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160298 Numerators of 1, 29/15, 391/225, -14761/3375, -955919/50625, ...
%t A160298 Table[15^n*HermiteH[n, 29/30], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)
%o A160298 (PARI) a(n)=numerator(polhermite(n, 29/30)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160298 (PARI) x='x+O('x^30); Vec(serlaplace(exp(29*x - 225*x^2))) \\ _G. C. Greubel_, Oct 04 2018
%o A160298 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(29/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 04 2018
%Y A160298 Cf. A001024 (denominators).
%K A160298 sign,frac
%O A160298 0,2
%A A160298 _N. J. A. Sloane_, Nov 12 2009