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.

A160152 Numerator of Hermite(n, 25/27).

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%I A160152 #17 Sep 08 2022 08:45:44
%S A160152 1,50,1042,-93700,-9242708,84323000,71595491320,2842116962000,
%T A160152 -588597736311920,-62580339060364000,4594562542866814240,
%U A160152 1142149470643447832000,-16580120530325575181120,-20812053164894042027728000,-726343053712911149403451520
%N A160152 Numerator of Hermite(n, 25/27).
%H A160152 G. C. Greubel, <a href="/A160152/b160152.txt">Table of n, a(n) for n = 0..376</a>
%F A160152 From _G. C. Greubel_, Sep 24 2018: (Start)
%F A160152 a(n) = 27^n * Hermite(n, 25/27).
%F A160152 E.g.f.: exp(50*x - 729*x^2).
%F A160152 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(50/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160152 Numerators of 1, 50/27, 1042/729, -93700/19683, -9242708/531441, ...
%t A160152 Numerator[HermiteH[Range[0,20],25/27]] (* _Harvey P. Dale_, Nov 15 2014 *)
%t A160152 Table[27^n*HermiteH[n, 25/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)
%o A160152 (PARI) a(n)=numerator(polhermite(n, 25/27)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160152 (PARI) x='x+O('x^30); Vec(serlaplace(exp(50*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018
%o A160152 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(50/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 24 2018
%Y A160152 Cf. A009971 (denominators).
%K A160152 sign,frac
%O A160152 0,2
%A A160152 _N. J. A. Sloane_, Nov 12 2009