A159486 Numerator of Hermite(n, 11/12).

1, 11, 49, -1045, -22079, 58091, 8587441, 69366539, -3565038335, -79170548149, 1439268811441, 72834751593131, -338718631136831, -66655130318970325, -416165794764599759, 62610547619111490251, 1138175082155994132481, -59607424953500501311861

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. A159280.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(11/6)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018

Mathematica

Numerator[Table[HermiteH[n,11/12],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)

PARI

a(n)=numerator(polhermite(n,11/12)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)

a(n) = 6^n * Hermite(n,11/12).

E.g.f.: exp(11*x-36*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/6)^(n-2*k)/(k!*(n-2*k)!)). (End)