A160310 Numerator of Hermite(n, 12/31).

1, 24, -1346, -124560, 4771596, 1072135584, -20123783544, -12846838359744, -37578736832880, 196631096935434624, 5369183316185589216, -3650389283510599332096, -201124616475050111174976, 79365587639487260327262720, 6930073770593296325672255616

Offset

0,2

Links

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

Formula

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

a(n) = 31^n * Hermite(n, 12/31).

a(n+2) = 24*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(24*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 24/31, -1346/961, -124560/29791, 4771596/923521, ...

Mathematica

Numerator/@HermiteH[Range[0, 20], 12/31] (* Harvey P. Dale, Jul 19 2011 *)
Table[31^n*HermiteH[n, 12/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 12/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(24*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/31)^(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: A186967 A068294 A003170 * A269271 A347857 A187852

Adjacent sequences: A160307 A160308 A160309 * A160311 A160312 A160313

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved