A159871 Numerator of Hermite(n, 7/23).
1, 14, -862, -41692, 2152300, 206572744, -8493648584, -1430234859088, 42880673385872, 12705837274723040, -230428050134150624, -137653751068447871936, 754569132502974755008, 1758215991420055828669568, 14236680031434866820993920, -25843381744473778798759726336
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..385
Programs
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Magma
[Numerator((&+[(-1)^k*Factorial(n)*(14/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018
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Mathematica
Numerator[Table[HermiteH[n, 7/23], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *) Table[23^n*HermiteH[n, 7/23], {n,0,30}] (* G. C. Greubel, Jul 14 2018 *) -
PARI
a(n)=numerator(polhermite(n, 7/23)) \\ Charles R Greathouse IV, Jan 29 2016
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PARI
x='x+O('x^30); Vec(serlaplace(exp(14*x - 529*x^2))) \\ G. C. Greubel, Jul 14 2018
Formula
From G. C. Greubel, Jul 14 2018: (Start)
a(n) = 23^n * Hermite(n, 7/23).
E.g.f.: exp(14*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/23)^(n-2*k)/(k!*(n-2*k)!)). (End)