A159515 Numerator of Hermite(n, 4/15).

1, 8, -386, -10288, 438796, 22028768, -811060856, -65966160448, 2027112412816, 253695076915328, -6180244656582176, -1191069803371633408, 21063652623108703936, 6600286159191690034688, -70420078571652397748096, -42145163431480866400519168, 138174222906806753595494656

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, A159514.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(8/15)^(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,4/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)

PARI

a(n)=numerator(polhermite(n,4/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 15^n * Hermite(n,4/15).

E.g.f.: exp(8*x-225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/15)^(n-2*k)/(k!*(n-2*k)!)). (End)