A159513 Numerator of Hermite(n, 1/15).
1, 2, -446, -2692, 596716, 6039032, -1330532936, -18966452272, 4153245843856, 76585719866912, -16667474227882976, -377970687856869952, 81748056052306991296, 2204537826531711723392, -473817052252932475634816, -14836222411655648808639232, 3168592657883982912917729536
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..412
Crossrefs
Cf. A159512.
Programs
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Magma
[Numerator((&+[(-1)^k*Factorial(n)*(2/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018
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Mathematica
Numerator[Table[HermiteH[n,1/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *) -
PARI
a(n)=numerator(polhermite(n,1/15)) \\ Charles R Greathouse IV, Jan 29 2016
Formula
From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 15^n * Hermite(n,1/15).
E.g.f.: exp(2*x-225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/15)^(n-2k)/(k!*(n-2k)!)). (End)