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A159670 Numerator of Hermite(n, 13/20). 1
1, 13, -31, -5603, -54239, 3777293, 103343809, -3189282083, -186141999679, 2683005336973, 369934668802849, -556859979508963, -821095451099884319, -9337776913476984947, 2013457072984498425089, 52320717306534037377757, -5360201893968552789356159 (list; graph; refs; listen; history; text; internal format)
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) -13*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, 13/20).
E.g.f.: exp(13*x - 100*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/10)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerator of 1, 13/10, -31/100, -5603/1000, -54239/10000, 3777293/100000,...
MAPLE
A159670 := proc(n)
orthopoly[H](n, 13/20) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 17 2014
MATHEMATICA
Numerator[Table[HermiteH[n, 13/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[10^n*HermiteH[n, 13/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 13/20)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/10)^(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: A180757 A214488 A247836 * A238736 A087511 A299449
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)