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A160192 Numerator of Hermite(n, 3/28). 1

%I

%S 1,3,-383,-3501,439905,6809283,-841785951,-18540791469,2254238275137,

%T 64906636872195,-7758232724066751,-277708714711204653,

%U 32620373362042216353,1404202914087633336771,-162020813910704234524575,-8192328034245044455772973,928105401692205765637182081

%N Numerator of Hermite(n, 3/28).

%H G. C. Greubel, <a href="/A160192/b160192.txt">Table of n, a(n) for n = 0..417</a>

%F From _G. C. Greubel_, Sep 24 2018: (Start)

%F a(n) = 14^n * Hermite(n, 3/28).

%F E.g.f.: exp(3*x - 196*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 3/14, -383/196, -3501/2744, 439905/38416, ...

%t Table[14^n*HermiteH[n, 3/28], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 3/28)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(3*x - 196*x^2))) \\ _G. C. Greubel_, Sep 24 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 24 2018

%Y Cf. A001023 (denominators)

%K sign,frac

%O 0,2

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

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Last modified February 7 06:02 EST 2023. Contains 360112 sequences. (Running on oeis4.)