A160231 Numerator of Hermite(n, 4/29).

1, 8, -1618, -39856, 7845580, 330915808, -63334001336, -3846274345024, 714924336969872, 57474862282401920, -10362725714790706976, -1049628989308325950208, 183334119260591052868288, 22652384474283979401944576, -3827564775957812126802428800

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 8/29, -1618/841, -39856/24389, 7845580/707281.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..371

Crossrefs

Cf. A009973 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(8/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018

Mathematica

Table[Numerator[HermiteH[n, 4/29]], {n, 0, 15}] (* Wesley Ivan Hurt, Jun 06 2014 *)
Table[29^n*HermiteH[n, 4/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

PARI

a(n)=numerator(polhermite(n, 4/29)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(8*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)

a(n) = 29^n * Hermite(n, 4/29).

E.g.f.: exp(8*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/29)^(n-2*k)/(k!*(n-2*k)!)). (End)