A159505 Numerator of Hermite(n, 11/13).
1, 22, 146, -11660, -404564, 6863912, 834719224, 4443809392, -1877181877360, -53314061897888, 4537477909175584, 280026043216724288, -10709769915546886976, -1371400569429065225600, 16887916481473586409344, 6861001657130755548544768, 65320299895805538972610816
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..422
Programs
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Magma
[Numerator((&+[(-1)^k*Factorial(n)*(22/13)^(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,11/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *) -
PARI
a(n)=numerator(polhermite(n,11/13)) \\ Charles R Greathouse IV, Jan 29 2016
Formula
From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 13^n * Hermite(n,11/13).
E.g.f.: exp(22*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/13)^(n-2*k)/(k!*(n-2*k)!)). (End)