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 A159745 Numerator of Hermite(n, 8/21). 1
 1, 16, -626, -38240, 1044556, 151623616, -2180514104, -837280401536, 66007653520, 5908906635694336, 94018537417467616, -50612259928144561664, -1721964008874583797056, 508128734937488699898880, 27874099084755797015426176, -5828388033652017714104551424 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x) FORMULA D-finite with recurrence a(n) -16*a(n-1) +882*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 17 2014 From G. C. Greubel, May 22 2018: (Start) a(n) = 21^n * Hermite(n,8/21). E.g.f.: exp(16*x-441*x^2). a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/21)^(n-2k)/(k!*(n-2k)!). (End) MATHEMATICA Numerator[Table[HermiteH[n, 8/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *) PROG (PARI) a(n)=numerator(polhermite(n, 8/21)) \\ Charles R Greathouse IV, Jan 29 2016 (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(16/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 22 2018 CROSSREFS Cf. A009965 (denominators). Sequence in context: A135786 A016792 A077204 * A091496 A139166 A128048 Adjacent sequences:  A159742 A159743 A159744 * A159746 A159747 A159748 KEYWORD sign,frac AUTHOR N. J. A. Sloane, Nov 12 2009 STATUS approved

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Last modified May 12 05:30 EDT 2021. Contains 343812 sequences. (Running on oeis4.)