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A159525
Numerator of Hermite(n, 9/16).
1
1, 9, -47, -2727, -6495, 1337769, 16196721, -881636103, -22446986943, 700772486985, 32165881341201, -607495851269991, -50757023589840927, 476300415242137833, 88746390990674543025, -54812825197840109511, -170886386128875683593599
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) -9*a(n-1) +128*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 16^n * Hermite(n,9/16).
E.g.f.: exp(18*x-252*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/8)^(n-2k)/(k!*(n-2k)!). (End)
EXAMPLE
Numerator of 1, 9/8, -47/64, -2727/512, -6495/4096, 1337769/32768...
MAPLE
A159525 := proc(n)
orthopoly[H](n, 9/16) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
MATHEMATICA
Numerator[Table[HermiteH[n, 9/16], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 9/16)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(9/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018
CROSSREFS
Cf. A001018 (denominators).
Sequence in context: A163614 A207318 A293042 * A173895 A392338 A341757
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved