A159753 Numerator of Hermite(n, 10/21).

1, 20, -482, -44920, 376972, 166017200, 1657897480, -845405072800, -27143960497520, 5422298983726400, 323914738103841760, -41346382274390012800, -3969548434571273011520, 358219141300718435244800, 52679225176808585054984320, -3369705453245099537303104000

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)*(20/21)^(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, 10/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[21^n*HermiteH[n, 10/21], {n,0,30}] (* G. C. Greubel, Jul 14 2018 *)

PARI

a(n)=numerator(polhermite(n, 10/21)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(20*x - 441*x^2))) \\ G. C. Greubel, Jul 14 2018

Formula

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

a(n) = 21^n * Hermite(n, 10/21).

E.g.f.: exp(20*x - 441*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/21)^(n-2*k)/(k!*(n-2*k)!)). (End)