A159745 Numerator of Hermite(n, 8/21).

1, 16, -626, -38240, 1044556, 151623616, -2180514104, -837280401536, 66007653520, 5908906635694336, 94018537417467616, -50612259928144561664, -1721964008874583797056, 508128734937488699898880, 27874099084755797015426176, -5828388033652017714104551424

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