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A160313 Numerator of Hermite(n, 15/31). 1

%I

%S 1,30,-1022,-145980,1513452,1167697800,20486660280,-12851291221200,

%T -661166264043120,177766465895877600,16769848012294217760,

%U -2913576034149940939200,-441955407700422580057920,53940055420621560419971200,12660899479421405397926325120

%N Numerator of Hermite(n, 15/31).

%H G. C. Greubel, <a href="/A160313/b160313.txt">Table of n, a(n) for n = 0..368</a>

%F From _G. C. Greubel_, Oct 04 2018: (Start)

%F a(n) = 31^n * Hermite(n, 15/31).

%F a(n+2) = 30*a(n+1) - 1922*(n+1)*a(n)

%F E.g.f.: exp(30*x - 961*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 30/31, -1022/961, -145980/29791, 1513452/923521, ...

%t Table[31^n*HermiteH[n, 15/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 15/31)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(30*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(30/31)^(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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Last modified January 29 16:53 EST 2023. Contains 359923 sequences. (Running on oeis4.)