A159492 Numerator of Hermite(n, 2/13).

1, 4, -322, -3992, 310540, 6639344, -498255224, -15457610528, 1117041417872, 46265544539200, -3212977815009824, -169229451802535296, 11268933708996384448, 731470391347068698368, -46589813151941838471040, -3647677144462096434561536, 221619644102496735309926656

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)*(4/13)^(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,2/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)

PARI

a(n)=numerator(polhermite(n,2/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 13^n * Hermite(n, 2/13).

E.g.f.: exp(4*x-169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/13)^(n-2*k)/(k!*(n-2*k)!)). (End)