A158969 Numerator of Hermite(n, 5/6).

1, 5, 7, -145, -1103, 4925, 123895, 87575, -15172895, -88475275, 2015632615, 26003712575, -269076694895, -6962185390675, 28153019652055, 1895235816710375, 1874863777497025, -536453596325102875, -3255976297539604025, 157531083721635311375, 1901199312366721133425

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
• DLMF, Digital library of mathematical functions, Table 18.9.1 for H_n(x).

Crossrefs

Cf. A158968.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(5/3)^(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,5/6],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
Table[3^n*HermiteH[n, 5/6], {n,0,30}] (* G. C. Greubel, Jul 14 2018 *)

PARI

a(n)=numerator(polhermite(n,5/6)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(5*x - 9*x^2))) \\ G. C. Greubel, Jul 14 2018

Formula

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

a(n) = 3^n * Hermite(n, 5/6).

E.g.f.: exp(5*x - 9*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/3)^(n-2*k)/(k!*(n-2*k)!)). (End)

D-finite with recurrence a(n) -5*a(n-1) +18*(n-1)*a(n-2)=0. - [DLMF] Georg Fischer, Feb 06 2021