A160328 Numerator of Hermite(n, 20/31).

1, 40, -322, -166640, -4808948, 1088770400, 89764806280, -8965108001600, -1566300023755120, 75195499682396800, 30101677798211937760, -241190391967188985600, -646057287688484347545920, -20279476307208127137958400, 15331208337896144822264021120

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 40/31, -322/961, -166640/29791, -4808948/923521, ...
		

Links

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

Crossrefs

Cf. A009975 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(40/31)^(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

Mathematica

Table[31^n*HermiteH[n, 20/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

PARI

a(n)=numerator(polhermite(n, 20/31)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(40*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

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

a(n) = 31^n * Hermite(n, 20/31).

a(n+2) = 40*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(40*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/31)^(n-2*k)/(k!*(n-2*k)!)). (End)