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A160312 Numerator of Hermite(n, 14/31). 1

%I

%S 1,28,-1138,-139496,2655820,1146808208,6588199624,-13040522665184,

%T -453772272366448,187805452873608640,13107905447855859424,

%U -3242599451690793996928,-367920121625910811856192,64485550348270970013174016,10998447568696594705407685760

%N Numerator of Hermite(n, 14/31).

%H G. C. Greubel, <a href="/A160312/b160312.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, 14/31).

%F a(n+2) = 28*a(n+1) - 1922*(n+1)*a(n)

%F E.g.f.: exp(28*x - 961*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 28/31, -1138/961, -139496/29791, 2655820/923521, ...

%t Table[31^n*HermiteH[n, 14/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 14/31)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(28*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/31)^(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 February 5 23:07 EST 2023. Contains 360091 sequences. (Running on oeis4.)