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A160246 Numerator of Hermite(n, 7/29). 1

%I

%S 1,14,-1486,-67900,6547756,548499784,-47387630984,-6198886653904,

%T 471157554050960,90008424571645664,-5872265109220393184,

%U -1596153412824165573056,86302501271257396667584,33424995502240561479908480,-1419140555765946374814673024

%N Numerator of Hermite(n, 7/29).

%H G. C. Greubel, <a href="/A160246/b160246.txt">Table of n, a(n) for n = 0..371</a>

%F From _G. C. Greubel_, Sep 26 2018: (Start)

%F a(n) = 29^n * Hermite(n, 7/29).

%F E.g.f.: exp(14*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 14/29, -1486/841, -67900/24389, 6547756/707281,...

%t Table[29^n*HermiteH[n, 7/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 7/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(14*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(14/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018

%Y Cf. A009973 (denominators)

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 12 2009

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Last modified June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)