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A159663
Numerator of Hermite(n, 11/20).
1
1, 11, -79, -5269, -10559, 4099051, 55648561, -4306727029, -125281982719, 5512661436491, 286146844695601, -7877707581330389, -716177841724956479, 11028541936218412331, 1983376349783289381041, -9062777573795371335349, -6049819602661617227811839
OFFSET
0,2
LINKS
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)
FORMULA
D-finite with recurrence a(n) -11*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 17 2014
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 10^n * Hermite(n, 11/20).
E.g.f.: exp(11*x - 100*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/10)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerator of 1, 11/10, -79/100, -5269/1000, -10559/10000, 4099051/100000,..
MAPLE
A159663 := proc(n)
orthopoly[H](n, 11/20) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 17 2014
MATHEMATICA
Numerator[Table[HermiteH[n, 11/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[10^n*HermiteH[n, 11/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 11/20)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(11/10)^(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
CROSSREFS
Cf. A011557 (denominators).
Sequence in context: A337929 A155619 A126506 * A227244 A026897 A021024
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved