A159868 Numerator of Hermite(n, 4/23).

1, 8, -994, -24880, 2955916, 128939488, -14605279736, -935350107712, 100683900863120, 8722274518579328, -888933907869994016, -99393135669529242368, 9550267734434756419264, 1338297392335821312458240, -120648003280729069290891136, -20788045001524017834458579968

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..385

Formula

From G. C. Greubel, Jul 14 2018: (Start)

a(n) = 23^n * Hermite(n, 4/23).

E.g.f.: exp(8*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 4/23], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[19^n*HermiteH[n, 4/23], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 4/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(8*x - 529*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018

Crossrefs

Cf. A159858, A159859.

Sequence in context: A301353 A183888 A181965 * A061105 A118545 A017091

Adjacent sequences: A159865 A159866 A159867 * A159869 A159870 A159871

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved