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A160064 Numerator of Hermite(n, 19/25). 1

%I

%S 1,38,194,-87628,-4057364,283960168,36149011384,-756038827408,

%T -345033325051504,-5550878077877152,3670691539870088224,

%U 208872254488527752512,-42534863002649658484544,-4749408611428603310092672,510713996558770024590318464,102521782569233818861053861632

%N Numerator of Hermite(n, 19/25).

%H G. C. Greubel, <a href="/A160064/b160064.txt">Table of n, a(n) for n = 0..380</a>

%F From _G. C. Greubel_, Sep 23 2018: (Start)

%F a(n) = 25^n * Hermite(n, 19/25).

%F E.g.f.: exp(38*x - 625*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 38/25, 194/625, -87628/15625, -4057364/390625, ...

%t Table[25^n*HermiteH[n, 19/25], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 19/25)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 625*x^2))) \\ _G. C. Greubel_, Sep 23 2018

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(38/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018

%Y Cf. A009969 (denominators).

%K sign,frac

%O 0,2

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

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Last modified September 20 21:32 EDT 2021. Contains 347591 sequences. (Running on oeis4.)