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.

A159761 Numerator of Hermite(n, 11/21).

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%I A159761 #21 Mar 18 2024 12:00:30
%S A159761 1,22,-398,-47564,6700,167953192,3665423224,-808168981136,
%T A159761 -40410040569968,4813419438356320,426670129688245024,
%U A159761 -33067616593161351872,-4867041163284902964032,242912748429751883004544,61149574443679238811690880,-1654195979849632997482909952
%N A159761 Numerator of Hermite(n, 11/21).
%H A159761 G. C. Greubel, <a href="/A159761/b159761.txt">Table of n, a(n) for n = 0..390</a>
%F A159761 From _G. C. Greubel_, May 22 2018: (Start)
%F A159761 a(n) = 21^n * Hermite(n,11/21).
%F A159761 E.g.f.: exp(22*x-441*x^2).
%F A159761 a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/21)^(n-2k)/(k!*(n-2k)!).
%F A159761 a(n+2) = 22*a(n+1) - 882*(n+1)*a(n). (End)
%t A159761 Numerator[Table[HermiteH[n, 11/21], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)
%o A159761 (PARI) a(n)=numerator(polhermite(n, 11/21)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159761 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, May 21 2018
%Y A159761 Cf. A009965 (denominators).
%K A159761 sign,frac
%O A159761 0,2
%A A159761 _N. J. A. Sloane_, Nov 12 2009