A159514 Numerator of Hermite(n, 2/15).

1, 4, -434, -5336, 564556, 11863024, -1222798904, -36921360416, 3704131105936, 147733421921344, -14410797291355424, -722443587811469696, 68443672240963470016, 4174970063145790238464, -383695602357053138639744, -27837093807246691056882176, 2478596940681121921590743296

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..412

Crossrefs

Cf. A159513.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(4/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 11 2018

Mathematica

Numerator[Table[HermiteH[n,2/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)

PARI

a(n)=numerator(polhermite(n,2/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)

a(n) = 15^n * Hermite(n,2/15).

E.g.f.: exp(4*x-225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/15)^(n-2*k)/(k!*(n-2*k)!)). (End)