A159521 Numerator of Hermite(n, 1/16).

1, 1, -127, -383, 48385, 244481, -30721919, -218483327, 27308356097, 251035282945, -31208190940799, -352533353110399, 43588599491534593, 585079829869107457, -71946349724044455295, -1120409404849485018239, 137016582065315869148161

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. A159513.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(1/8)^(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,1/16],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)

PARI

a(n)=numerator(polhermite(n,1/16)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 8^n * Hermite(n,1/16).

E.g.f.: exp(2*x-64*x^2).

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