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.

A159869 Numerator of Hermite(n, 5/23).

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%I A159869 #16 Sep 08 2022 08:45:44
%S A159869 1,10,-958,-30740,2733292,157424600,-12884868680,-1128180047600,
%T A159869 84143536968080,10390351292567200,-697311246084385760,
%U A159869 -116903029136204833600,6946277990568033138880,1553663637818936898774400,-80002471104083358804411520,-23812890514414926932690528000
%N A159869 Numerator of Hermite(n, 5/23).
%H A159869 Robert Israel, <a href="/A159869/b159869.txt">Table of n, a(n) for n = 0..385</a>
%F A159869 a(n) = 10*a(n-1) + 1058*(1-n)*a(n-2). - _Robert Israel_, Dec 07 2017
%F A159869 From _G. C. Greubel_, Jul 11 2018: (Start)
%F A159869 a(n) = 23^n * Hermite(n, 5/23).
%F A159869 E.g.f.: exp(10*x - 529*x^2).
%F A159869 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A159869 Numerators of 1, 10/23, -958/529, -30740/12167, 2733292/279841
%p A159869 f:= gfun:-rectoproc({a(n) = -(1058*n-1058)*a(n-2)+10*a(n-1), a(0) = 1, a(1) = 10},a(n),remember):
%p A159869 map(f, [$0..40]); # _Robert Israel_, Dec 07 2017
%t A159869 Numerator[Table[HermiteH[n, 5/23], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *)
%t A159869 Table[23^n*HermiteH[n, 5/23], {n,0,30}] (* _G. C. Greubel_, Jul 11 2018 *)
%o A159869 (PARI) a(n)=numerator(polhermite(n, 5/23)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159869 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 11 2018
%Y A159869 Cf. A009967 (denominators)
%K A159869 sign,frac
%O A159869 0,2
%A A159869 _N. J. A. Sloane_, Nov 12 2009