A159776 Numerator of Hermite(n, 17/21).

1, 34, 274, -50660, -2447444, 95515384, 14040751096, -28081874864, -87642381012080, -2781695245370336, 601127582131299616, 44972889856630550464, -4303061546712430158656, -622297158830800371505280, 28180800294357511567970176, 8642272527250878380658183424

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)*(34/21)^(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, 17/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[21^n*HermiteH[n, 17/21], {n,0,50}] (* G. C. Greubel, Jul 11 2018 *)

PARI

a(n)=numerator(polhermite(n, 17/21)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 21^n * Hermite(n, 17/21).

E.g.f.: exp(34*x - 441*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(37/21)^(n-2*k)/(k!*(n-2*k)!)). (End)