A159017 Numerator of Hermite(n, 3/8).

1, 3, -23, -261, 1425, 37683, -114951, -7579989, 3009057, 1949504355, 4981904649, -608895679653, -3580317475407, 223074988560531, 2158637035450905, -93461683768765173, -1316530828322729919, 43902789604639578819, 847901139421483812393

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. A159014.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(3/4)^(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,3/8],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
Table[4^n*HermiteH[n, 3/8], {n,0,30}] (* G. C. Greubel, Jul 09 2018 *)

PARI

a(n)=numerator(polhermite(n,3/8)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 4^n * Hermite(n, 3/8).

E.g.f.: exp(3*x - 16*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/4)^(n-2*k)/(k!*(n-2*k)!)). (End)