A159247 Numerator of Hermite(n, 1/10).
1, 1, -49, -149, 7201, 37001, -1763249, -12863549, 604273601, 5749693201, -266173427249, -3141020027749, 143254364959201, 2027866381608601, -91087470841872049, -1510593937967892749, 66805009193436144001, 1275280159567750343201, -55508977654852972057649
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..450 (terms 0..100 from T. D. Noe)
Programs
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Magma
[Numerator((&+[(-1)^k*Factorial(n)*(1/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 10 2018
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Mathematica
Numerator[Table[HermiteH[n,1/10],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*) -
PARI
a(n)=numerator(polhermite(n,1/10)) \\ Charles R Greathouse IV, Jan 29 2016
Formula
From G. C. Greubel, Jun 10 2018: (Start)
a(n) = 5^n * Hermite(n,1/10).
E.g.f.: exp(x-25*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/5)^(n-2*k)/(k!*(n-2*k)!)). (End)
a(n) = 50*(1-n)*a(n-2)+a(n-1) for n>1. - Christian Krause, Oct 21 2024