A159528 Numerator of Hermite(n, 15/16).

1, 15, 97, -2385, -73023, 125775, 48621345, 632724975, -34073850495, -1159018131825, 21867803792865, 1811560265628975, -3616463755919295, -2836803524344895025, -36534257175323718495, 4535538057996196107375, 138178844646564481121025

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. A159521.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(15/8)^(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,15/16],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)

PARI

a(n)=numerator(polhermite(n,15/16)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 8^n * Hermite(n, 15/16).

E.g.f.: exp(15*x-64*x^2).

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