A159544 Numerator of Hermite(n, 16/17).

1, 32, 446, -22720, -1500404, 4515712, 4480670344, 127720961792, -14041721434480, -1039916813229568, 39767696878818784, 7283285480589104128, -19777881376678496576, -51149760297419738122240, -1488181328853069396639616, 366282057803422300192698368

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..404

Formula

From G. C. Greubel, Jul 02 2018: (Start)

a(n) = 17^n * Hermite(n, 16/17).

E.g.f.: exp(32*x-289*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/17)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 16/17], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 08 2011 *)
Table[17^n*HermiteH[n, 16/17], {n, 0, 50)] (* G. C. Greubel, Jul 02 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 16/17)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/17)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 02 2018

Crossrefs

Cf. A159542, A159543.

Sequence in context: A125444 A022692 A160142 * A135217 A274802 A274748

Adjacent sequences: A159541 A159542 A159543 * A159545 A159546 A159547

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved