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.

A159014 Numerator of Hermite(n, 1/8).

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%I A159014 #13 Sep 08 2022 08:45:43
%S A159014 1,1,-31,-95,2881,15041,-445919,-3333791,96552065,950002561,
%T A159014 -26856992159,-330857811679,9122803428289,136172203113025,
%U A159014 -3658914023055199,-64664061017690399,1691614670048805121,34799613911106289409,-885438766595443696415
%N A159014 Numerator of Hermite(n, 1/8).
%H A159014 G. C. Greubel, <a href="/A159014/b159014.txt">Table of n, a(n) for n = 0..450</a>
%F A159014 From _G. C. Greubel_, Jun 10 2018: (Start)
%F A159014 a(n) = 4^n * Hermite(n,1/8).
%F A159014 E.g.f.: exp(x-16*x^2).
%F A159014 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/4)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t A159014 Numerator[Table[HermiteH[n,1/8],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*)
%o A159014 (PARI) a(n)=numerator(polhermite(n,1/8)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159014 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/4)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 10 2018
%Y A159014 Cf. A158811, A158954, A158960, A158980.
%K A159014 sign,frac
%O A159014 0,3
%A A159014 _N. J. A. Sloane_, Nov 12 2009