A159784 Numerator of Hermite(n, 19/21).

1, 38, 562, -45676, -3222740, 38680808, 15682154104, 391223020016, -81955144677488, -5874765126977440, 427318863624757024, 68053545237681787712, -1559812895855484713792, -779551612838132460267904, -11738146623970045761841280, 9179853743614397880438109952

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..390

Crossrefs

Cf. A009965 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(38/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 21 2018

Mathematica

Numerator[Table[HermiteH[n, 19/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[21^n*HermiteH[n, 19/21], {n,0,50}] (* G. C. Greubel, Jul 11 2018 *)

PARI

a(n)=numerator(polhermite(n, 19/21)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 21^n * Hermite(n, 19/21).

E.g.f.: exp(38*x - 441*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/21)^(n-2*k)/(k!*(n-2*k)!)). (End)