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.

A159762 Numerator of Hermite(n, 13/21).

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%I A159762 #17 Sep 08 2022 08:45:44
%S A159762 1,26,-206,-51220,-786644,160251416,7635636856,-649523935216,
%T A159762 -64030044264560,2918259736005536,584145244508221216,
%U A159762 -10551274514355075904,-5941710299591994211136,-42809778329457726121600,67014596058555904745723776,2270994640334597525538334976
%N A159762 Numerator of Hermite(n, 13/21).
%H A159762 G. C. Greubel, <a href="/A159762/b159762.txt">Table of n, a(n) for n = 0..390</a>
%F A159762 From _G. C. Greubel_, May 22 2018: (Start)
%F A159762 a(n) = 21^n * Hermite(n,13/21).
%F A159762 E.g.f.: exp(26*x-441*x^2).
%F A159762 a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/21)^(n-2k)/(k!*(n-2k)!).
%F A159762 a(n+2) = 26*a(n+1) - 882*(n+1)*a(n). (End)
%t A159762 Numerator[Table[HermiteH[n, 13/21], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)
%o A159762 (PARI) a(n)=numerator(polhermite(n, 13/21)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159762 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/21)^(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 A159762 Cf. A009965 (denominators).
%K A159762 sign,frac
%O A159762 0,2
%A A159762 _N. J. A. Sloane_, Nov 12 2009