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.

A159013 Numerator of Hermite(n, 6/7).

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%I A159013 #13 Sep 08 2022 08:45:43
%S A159013 1,12,46,-1800,-35124,284112,20620104,80383392,-13180790640,
%T A159013 -221190067008,8971176540384,324420384152448,-5777883700704576,
%U A159013 -450852976171733760,1950788120636824704,641979740755260615168,4836098351726995067136
%N A159013 Numerator of Hermite(n, 6/7).
%H A159013 G. C. Greubel, <a href="/A159013/b159013.txt">Table of n, a(n) for n = 0..450</a>
%F A159013 From _G. C. Greubel_, Jul 14 2018: (Start)
%F A159013 a(n) = 7^n * Hermite(n, 6/7).
%F A159013 E.g.f.: exp(12*x - 49*x^2).
%F A159013 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/7)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t A159013 Numerator[Table[HermiteH[n,6/7],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*)
%t A159013 Table[7^n*HermiteH[n, 6/7], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018~ *)
%o A159013 (PARI) a(n)=numerator(polhermite(n,6/7)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159013 (PARI) x='x+O('x^30); Vec(serlaplace(exp(12*x - 49*x^2))) \\ _G. C. Greubel_, Jul 14 2018
%o A159013 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(12/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 14 2018
%Y A159013 Cf. A158980, A158981.
%K A159013 sign,frac
%O A159013 0,2
%A A159013 _N. J. A. Sloane_, Nov 12 2009