A159857 Numerator of Hermite(n, 21/22).
1, 21, 199, -5985, -270159, 120141, 329415351, 6743277639, -416420774175, -21799821766779, 449168189050791, 62188100645671791, 110264394305901969, -178278691994606939715, -4090744316373113328489, 518102577833892931856151, 25729556002946152951394241
Offset: 0
Examples
Numerators of 1, 21/11, 199/121, -5985/1331, -270159/14641
Links
- Robert Israel, Table of n, a(n) for n = 0..435
Programs
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Magma
[Numerator((&+[(-1)^k*Factorial(n)*(21/22)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018
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Maple
f:= gfun:-rectoproc({a(n) = 21*a(n-1)+242*(1-n)*a(n-2), a(0)=1, a(1)=21}, a(n), remember): map(f, [$0..40]); # Robert Israel, Dec 07 2017 -
Mathematica
Numerator[Table[HermiteH[n,21/22],{n,0,30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *) Table[11^n*HermiteH[n, 21/22], {n,0,30}] (* G. C. Greubel, Jul 11 2018 *) -
PARI
a(n)=numerator(polhermite(n, 21/22)) \\ Charles R Greathouse IV, Jan 29 2016
Formula
a(n) = 21*a(n-1) + 242*(1-n)*a(n-2). - Robert Israel, Dec 07 2017
From G. C. Greubel, Jun 02 2018: (Start)
a(n) = 11^n * Hermite(n, 21/22).
E.g.f.: exp(21*x - 121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(21/11)^(n-2*k)/(k!*(n-2*k)!)). (End)