A159512 Numerator of Hermite(n, 13/14).
1, 13, 71, -1625, -41999, 91013, 21762679, 229399183, -11947008415, -335160068867, 6180180526759, 408799214337527, -1347844821458351, -498269858739890315, -4760353861080634921, 621741645997081258207, 15080361573750589690561
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..450
Programs
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Magma
[Numerator((&+[(-1)^k*Factorial(n)*(13/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 11 2018
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Mathematica
Numerator[Table[HermiteH[n,13/14],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *) -
PARI
a(n)=numerator(polhermite(n,13/14)) \\ Charles R Greathouse IV, Jan 29 2016
Formula
From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 7^n * Hermite(n,13/14).
E.g.f.: exp(13*x-49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/7)^(n-2*k)/(k!*(n-2*k)!)). (End)