A159498 Numerator of Hermite(n, 6/13).

1, 12, -194, -10440, 71436, 14972112, 58938504, -29656181088, -495322673520, 74246441579712, 2397728871804384, -222180226077773952, -11580918658301987136, 762191973071827303680, 60032860261440859119744, -2886298093438596491576832, -339002178646768313636024064

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..422

Crossrefs

Cf. A159280, A159488.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(12/13)^(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,6/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)

PARI

a(n)=numerator(polhermite(n,6/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 13^n * Hermite(n,6/13).

E.g.f.: exp(12*x-169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/13)^(n-2*k)/(k!*(n-2*k)!)). (End)