A160306 Numerator of Hermite(n, 8/31).

1, 16, -1666, -88160, 8195596, 808903616, -65817219704, -10381352014976, 719403241658000, 171134120448798976, -9706091347019300384, -3444495256578225124864, 150094259153430446720704, 81845346744175071427394560, -2440729611300811998925197184

Offset

0,2

Links

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

Formula

a(n+2) = 16*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, 8/31).

E.g.f.: exp(16*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 16/31, -1666/961, -88160/29791, 8195596/923521, ...

Mathematica

Table[31^n*HermiteH[n, 8/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 8/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(16*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Maxima) makelist(num(hermite(n, 8/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/31)^(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: A307924 A263387 A264199 * A167000 A075413 A265213

Adjacent sequences: A160303 A160304 A160305 * A160307 A160308 A160309

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved