A160296 Numerator of Hermite(n, 19/30).

1, 19, -89, -18791, -236879, 29323099, 1090116631, -58460151311, -4544610262559, 124108949730979, 20763741608252551, -163979183232607031, -105896125442269661039, -1126538793947045592341, 598088096752283650823671, 18460868240159776597398049

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 19/15, -89/225, -18791/3375, -236879/50625, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..412

Crossrefs

Cf. A001024 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(19/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018

Mathematica

Numerator[HermiteH[Range[0,20],19/30]] (* Harvey P. Dale, Sep 10 2011 *)
Table[15^n*HermiteH[n, 19/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

PARI

a(n)=numerator(polhermite(n, 19/30)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(19*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)

a(n) = 15^n * Hermite(n, 19/30).

E.g.f.: exp(19*x - 225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/15)^(n-2*k)/(k!*(n-2*k)!)). (End)