A159496 Numerator of Hermite(n, 4/13).

1, 8, -274, -7600, 217036, 12011488, -270698936, -26524889152, 428274569360, 75149496821888, -701615265418016, -259618221381325568, 531659785773578944, 1057264784208845135360, 6122005174981655202944, -4954000917476401938899968, -70670573576968207390125824

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..422

Crossrefs

Cf. A159280, A159488.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(8/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018

Mathematica

Numerator[Table[HermiteH[n,4/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)

PARI

a(n)=numerator(polhermite(n,4/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)

a(n) = 13^n * Hermite(n,4/13).

E.g.f.: exp(8*x-169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/13)^(n-2*k)/(k!*(n-2*k)!)). (End)