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.

A160281 Numerator of Hermite(n, 19/29).

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%I A160281 #13 Sep 08 2022 08:45:45
%S A160281 1,38,-238,-136876,-4000340,768888808,62860634104,-5370921754384,
%T A160281 -944216132607088,36390910087921760,15676398398747125024,
%U A160281 -16391968526453252288,-290667617977624530780992,-10714513990411799725496704,5948586603063089600488296320
%N A160281 Numerator of Hermite(n, 19/29).
%H A160281 G. C. Greubel, <a href="/A160281/b160281.txt">Table of n, a(n) for n = 0..371</a>
%F A160281 From _G. C. Greubel_, Oct 03 2018: (Start)
%F A160281 a(n) = 29^n * Hermite(n, 19/29).
%F A160281 E.g.f.: exp(38*x - 841*x^2).
%F A160281 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160281 Numerators of 1, 38/29, -238/841, -136876/24389, -4000340/707281, ...
%t A160281 Table[29^n*HermiteH[n, 19/29], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)
%o A160281 (PARI) a(n)=numerator(polhermite(n, 19/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160281 (PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 841*x^2))) \\ _G. C. Greubel_, Oct 03 2018
%o A160281 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 03 2018
%Y A160281 Cf. A009973 (denominators).
%K A160281 sign,frac
%O A160281 0,2
%A A160281 _N. J. A. Sloane_, Nov 12 2009