A159485 Numerator of Hermite(n, 7/12).

1, 7, -23, -1169, -3215, 314167, 3356569, -112224161, -2477279903, 47300157415, 1936378479049, -20501463985457, -1677122003305007, 5973410860299799, 1611600071115585145, 5260002350626898623, -1703708060350443666239, -17985479130375292877369

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. A159280.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(7/6)^(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,7/12],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)

PARI

a(n)=numerator(polhermite(n,7/12)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 6^n * Hermite(n,7/12).

E.g.f.: exp(7*x-36*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/6)^(n-2*k)/(k!*(n-2*k)!)). (End)