A159028 Numerator of Hermite(n, 7/8).

1, 7, 17, -329, -3935, 14567, 731569, 2324119, -147602623, -1628192825, 31112205649, 738807143543, -5779846383647, -324160867806041, 135290020954865, 146171098923790423, 958258482408197761, -68131793272123312249, -998215167334922767727

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. A159014, A159017.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(7/4)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018

Mathematica

Numerator[Table[HermiteH[n,7/8],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011 *)
Table[4^n*HermiteH[n, 7/8], {n,0,30}] (* G. C. Greubel, Jul 14 2018 *)

PARI

a(n)=numerator(polhermite(n,7/8)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(7*x - 16*x^2))) \\ G. C. Greubel, Jul 14 2018

Formula

From G. C. Greubel, Jul 14 2018: (Start)

a(n) = 4^n * Hermite(n, 7/8).

E.g.f.: exp(7*x - 16*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/4)^(n-2*k)/(k!*(n-2*k)!)). (End)