A160184 Numerator of Hermite(n, 1/28).

1, 1, -391, -1175, 458641, 2301041, -896635319, -6308683751, 2454058631585, 22238090874721, -8635680761357159, -95808996990263479, 37141246445981806129, 487826768288181211345, -188783965120435102822039, -2865977269485973590683399, 1107183737638672431002905921

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 1/14, -391/196, -1175/2744, 458641/38416, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..417

Crossrefs

Cf. A001023 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(1/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018

Mathematica

Table[14^n*HermiteH[n, 1/28], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PARI

a(n)=numerator(polhermite(n, 1/28)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(x - 196*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)

a(n) = 14^n * Hermite(n, 1/28).

E.g.f.: exp(x - 196*x^2).

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