A159501 Numerator of Hermite(n, 8/13).

1, 16, -82, -12128, -110900, 14622656, 421383496, -22912610432, -1363595118448, 40138176712960, 4790267177726176, -59022762446185984, -18754577565924898112, -60676916573068018688, 81436783159504914005120, 1590111699775836488513536, -387442703422276530189741824

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)*(16/13)^(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,8/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)

PARI

a(n)=numerator(polhermite(n,8/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 13^n * Hermite(n,8/13).

E.g.f.: exp(16*x-169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/13)^(n-2*k)/(k!*(n-2*k)!)). (End)