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A159520
Numerator of Hermite(n, 14/15).
1
1, 28, 334, -15848, -894644, 3476368, 2110287304, 49701850912, -5255753182064, -326087752380992, 12155343320691424, 1807744498693823872, -9552103473995480384, -10029279190218522359552, -224940012003245065821056, 56886138562285829022188032
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) -28*a(n-1) +450*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 15^n * Hermite(n,14/15).
E.g.f.: exp(28*x-225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/15)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 28/15, 334/225, -15848/3375, -894644/50625, 3476368/759375
MAPLE
A159520 := proc(n)
orthopoly[H](n, 14/15) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
MATHEMATICA
Numerator[Table[HermiteH[n, 14/15], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 14/15)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/15)^(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
CROSSREFS
Cf. A001024 (denominators).
Sequence in context: A125416 A241038 A055753 * A027820 A092713 A134288
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved