A159646 Numerator of Hermite(n, 8/19).

1, 16, -466, -30560, 520396, 96583616, -333291704, -423732891776, -5095269996400, 2365956862955776, 70964374243899616, -15946778562638308864, -818747517247263692096, 125062929190742088924160, 9685771063934690436799616, -1109163751237065987856615424

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..396

Formula

From G. C. Greubel, Jul 10 2018: (Start)

a(n) = 19^n * Hermite(n, 8/19).

E.g.f.: exp(16*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 8/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)
Table[19^n*HermiteH[n, 8/19], {n, 0, 50}] (* G. C. Greubel, Jul 10 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 8/19)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 2018

Crossrefs

Cf. A159564, A159618.

Sequence in context: A358569 A368772 A253446 * A113674 A281834 A299078

Adjacent sequences: A159643 A159644 A159645 * A159647 A159648 A159649

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved