A159449 Numerator of Hermite(n, 6/11).

1, 12, -98, -6984, -12660, 6608592, 94621704, -8460215136, -261811748208, 13237235524800, 729072813894624, -23285236203280512, -2220214665026855232, 40977749954004344064, 7476528335622538688640, -49114276816696253425152, -27729169180110170480865024

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..435

Crossrefs

Cf. A159280.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(12/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 15 2018

Mathematica

Numerator[Table[HermiteH[n,6/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

PARI

a(n)=numerator(polhermite(n,6/11)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 15 2018: (Start)

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

E.g.f.: exp(12*x-121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/11)^(n-2*k)/(k!*(n-2*k)!)). (End)