A158961 Numerator of Hermite(n, 2/5).

1, 4, -34, -536, 2956, 119024, -262904, -36758816, -55018864, 14483450944, 82692292576, -6910956301696, -73124586123584, 3854075436523264, 62947282726422656, -2446063674660594176, -56994716743459368704, 1728872072754637865984

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. A158954, A158960.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(4/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018

Mathematica

Numerator[Table[HermiteH[n,2/5],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011 *)
Table[5^n*HermiteH[n, 2/5], {n,0,30}] (* G. C. Greubel, Jul 09 2018 *)

PARI

a(n)=numerator(polhermite(n,2/5)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 5^n * Hermite(n, 2/5).

E.g.f.: exp(4*x-25*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/5)^(n-2*k)/(k!*(n-2*k)!)). (End)