A159014 Numerator of Hermite(n, 1/8).

1, 1, -31, -95, 2881, 15041, -445919, -3333791, 96552065, 950002561, -26856992159, -330857811679, 9122803428289, 136172203113025, -3658914023055199, -64664061017690399, 1691614670048805121, 34799613911106289409, -885438766595443696415

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. A158811, A158954, A158960, A158980.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(1/4)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 10 2018

Mathematica

Numerator[Table[HermiteH[n,1/8],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)

PARI

a(n)=numerator(polhermite(n,1/8)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 10 2018: (Start)

a(n) = 4^n * Hermite(n,1/8).

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

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