A159497 Numerator of Hermite(n, 5/13).

1, 10, -238, -9140, 149932, 13856600, -114819080, -29249375600, -20831812720, 78881993495200, 852190309246240, -258099234921313600, -5749435918990656320, 989356137650941398400, 35156582804554357854080, -4330067415318711118688000, -221544548972277705507065600

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)*(10/13)^(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,5/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)

PARI

a(n)=numerator(polhermite(n,5/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 13^n * Hermite(n,5/13).

E.g.f.: exp(10*x-169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/13)^(n-2*k)/(k!*(n-2*k)!)). (End)