A160305 Numerator of Hermite(n, 7/31).

1, 14, -1726, -77980, 8860396, 723555784, -75018624584, -9394306045264, 877780290519440, 156735773819251424, -12989542631935753184, -3194315169653112913856, 229904497949242113022144, 76892348044168785827484800, -4667900913141400434386502784

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..368

Formula

a(n+2) = 14*a(n+1) - 1922*(n+1)*a(n). - Bruno Berselli, Mar 28 2018

From G. C. Greubel, Oct 04 2018: (Start)

a(n) = 31^n * Hermite(n, 7/31).

E.g.f.: exp(14*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 14/31, -1726/961, -77980/29791, 8860396/923521, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 7/31]] (* Harvey P. Dale, Apr 23 2016 *)
Table[31^n*HermiteH[n, 7/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 7/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(14*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Maxima) makelist(num(hermite(n, 7/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(14/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018

Crossrefs

Cf. A009975 (denominators).

Sequence in context: A322848 A206644 A060614 * A279804 A198601 A233076

Adjacent sequences: A160302 A160303 A160304 * A160306 A160307 A160308

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved