A159472 Numerator of Hermite(n, 1/12).

1, 1, -71, -215, 15121, 77041, -5366519, -38648231, 2666077345, 24927458401, -1702690661159, -19650460709879, 1328880542928049, 18306878596263505, -1225525309584390359, -19678858934618003399, 1303888475416523584321, 23973933968096463499969

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

• T. D. Noe, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A159280.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(1/6)^(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,1/12],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)

PARI

a(n)=numerator(polhermite(n,1/12)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 6^n * Hermite(n,1/12).

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

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