A159527 Numerator of Hermite(n, 13/16).

1, 13, 41, -2795, -52079, 754013, 43132729, -18356507, -38885559775, -486715213907, 38468867080009, 1123090745841077, -39563985152718671, -2239399192597236995, 36722281790359787609, 4490393016408925933957, -12131671824174755067839

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..450

Crossrefs

Cf. A159521.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(13/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

Mathematica

Numerator[Table[HermiteH[n,13/16],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)

PARI

a(n)=numerator(polhermite(n,13/16)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 09 2018: (Start)

a(n) = 16^n * Hermite(n,13/16).

E.g.f.: exp(26*x-252*x^2).

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