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%I #37 Sep 08 2022 08:45:45
%S 1,18,-1598,-97956,7450860,887201208,-55633142856,-11232600902064,
%T 546301487747472,182545898249590560,-6164096966563140576,
%U -3619485909755267093568,65170591691483110373568,84652893673042176232776576,-104600317888637823603991680
%N Numerator of Hermite(n, 9/31).
%H G. C. Greubel, <a href="/A160307/b160307.txt">Table of n, a(n) for n = 0..368</a>
%F From _Vincenzo Librandi_, Jan 19 2017: (Start)
%F E.g.f.: exp(18*x - 961*x^2).
%F a(n+2) = -1922*(n+1)*a(n)+18*a(n+1). (End)
%F From _G. C. Greubel_, Oct 04 2018: (Start)
%F a(n) = 31^n * Hermite(n, 9/31).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 18/31, -1598/961, -97956/29791, 7450860/923521, ...
%t Numerator[HermiteH[Range[0,20],9/31]] (* _Harvey P. Dale_, Jan 18 2017 *)
%t Table[31^n*HermiteH[n, 9/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 9/31)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018
%o (Sage) [numerator(hermite(n, 9/31)) for n in range(20)] # _Bruno Berselli_, Jan 19 2017
%o (Maxima) makelist(num(hermite(n, 9/31)), n, 0, 20); /* _Bruno Berselli_, Jan 19 2017 */
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 04 2018
%Y Cf. A009975 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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