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A159676
Numerator of Hermite(n, 17/20).
1
1, 17, 89, -5287, -143279, 1793857, 173774569, 801539273, -229658228959, -5186652729103, 325211715731449, 15901904625640633, -445133395973297039, -45731838833083568863, 379905569368151630729, 134507543411892570538793, 1146911529897718806972481
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) -17*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, 17/20).
E.g.f.: exp(17*x - 100*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/10)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerator of 1, 17/10, 89/100, -5287/1000, -143279/10000, 1793857/100000,...
MAPLE
A159676 := proc(n)
orthopoly[H](n, 17/20) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 17 2014
MATHEMATICA
Numerator/@Table[HermiteH[n, 17/20], {n, 0, 35}] (* Harvey P. Dale, Mar 13 2011 *)
Table[10^n*HermiteH[n, 17/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 17/20)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(17/10)^(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: A267820 A200670 A057638 * A061971 A061222 A371492
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved