A159532 Numerator of Hermite(n, 4/17).

1, 8, -514, -13360, 784396, 37163488, -1969596536, -144639748672, 6811869595280, 723309154621568, -29648872397674016, -4417917892894055168, 153164187561258952384, 31867992005603238264320, -895931769290473862098816, -265043245463665194931667968

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jul 09 2018: (Start)

a(n) = 17^n * Hermite(n, 4/17).

E.g.f.: exp(8*x-289*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/17)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 4/17], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
Table[17^n*HermiteH[n, 417], {n, 0, 30}] (* G. C. Greubel, Jul 09 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 4/17)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/17)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018

Crossrefs

Cf. A159529, A159530.

Sequence in context: A107672 A091112 A015480 * A003397 A272357 A241367

Adjacent sequences: A159529 A159530 A159531 * A159533 A159534 A159535

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved