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.

A159943 Numerator of Hermite(n, 19/23).

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%I A159943 #16 Sep 08 2022 08:45:44
%S A159943 1,38,386,-65740,-3723284,136726888,24891794104,77945890928,
%T A159943 -181386683278960,-7552427985415072,1440171734736484384,
%U A159943 134631214005677868352,-11644732516647446263616,-2151777728648689174614400,78394097345318787274427264,34851107415866497970816728832
%N A159943 Numerator of Hermite(n, 19/23).
%H A159943 G. C. Greubel, <a href="/A159943/b159943.txt">Table of n, a(n) for n = 0..385</a>
%F A159943 From _G. C. Greubel_, Jul 16 2018: (Start)
%F A159943 a(n) = 23^n * Hermite(n, 19/23).
%F A159943 E.g.f.: exp(38*x - 529*x^2).
%F A159943 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A159943 Numerators of 1, 38/23, 386/529, -65740/12167, -3723284/279841, ...
%t A159943 Numerator[HermiteH[Range[0,20],19/23]] (* _Harvey P. Dale_, Jan 18 2012 *)
%t A159943 Table[23^n*HermiteH[n,19/23], {n,0,30}] (* _G. C. Greubel_, Jul 16 2018 *)
%o A159943 (PARI) a(n)=numerator(polhermite(n, 19/23)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159943 (PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 529*x^2))) \\ _G. C. Greubel_, Jul 16 2018
%o A159943 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 16 2018
%Y A159943 Cf. A009967 (denominators).
%K A159943 sign,frac
%O A159943 0,2
%A A159943 _N. J. A. Sloane_, Nov 12 2009