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 A159761 Numerator of Hermite(n, 11/21). 1

%I #21 Mar 18 2024 12:00:30

%S 1,22,-398,-47564,6700,167953192,3665423224,-808168981136,

%T -40410040569968,4813419438356320,426670129688245024,

%U -33067616593161351872,-4867041163284902964032,242912748429751883004544,61149574443679238811690880,-1654195979849632997482909952

%N Numerator of Hermite(n, 11/21).

%H G. C. Greubel, <a href="/A159761/b159761.txt">Table of n, a(n) for n = 0..390</a>

%F From _G. C. Greubel_, May 22 2018: (Start)

%F a(n) = 21^n * Hermite(n,11/21).

%F E.g.f.: exp(22*x-441*x^2).

%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/21)^(n-2k)/(k!*(n-2k)!).

%F a(n+2) = 22*a(n+1) - 882*(n+1)*a(n). (End)

%t Numerator[Table[HermiteH[n, 11/21], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)

%o (PARI) a(n)=numerator(polhermite(n, 11/21)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (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 Cf. A009965 (denominators).

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 12 2009

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Last modified August 11 10:58 EDT 2024. Contains 375068 sequences. (Running on oeis4.)