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%I A160008 #12 Sep 08 2022 08:45:44
%S A160008 1,8,-1186,-29488,4211596,181132768,-24873412856,-1557483062848,
%T A160008 205182497987216,17216290612377728,-2170572777457158176,
%U A160008 -232568214874378865408,27984829971040893996736,3712401862884010133093888,-425054272126342446382208896,-68367466777480916900200711168
%N A160008 Numerator of Hermite(n, 4/25).
%H A160008 G. C. Greubel, <a href="/A160008/b160008.txt">Table of n, a(n) for n = 0..380</a>
%F A160008 From _G. C. Greubel_, Jul 17 2018: (Start)
%F A160008 a(n) = 25^n * Hermite(n, 4/25).
%F A160008 E.g.f.: exp(8*x - 625*x^2).
%F A160008 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160008 Numerators of 1, 8/25, -1186/625, -29488/15625, 4211596/390625
%p A160008 seq(coeff(series(factorial(n)*exp(8*x-625*x^2), x,n+1),x,n),n=0..15); # _Muniru A Asiru_, Jul 17 2018
%t A160008 Numerator[Table[HermiteH[n, 4/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 4/25], {n, 0, 30}] (* _G. C. Greubel_, Jul 17 2018 *)
%o A160008 (PARI) a(n)=numerator(polhermite(n, 4/25)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160008 (PARI) x='x+O('x^30); Vec(serlaplace(exp(8*x - 625*x^2))) \\ _G. C. Greubel_, Jul 17 2018
%o A160008 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 17 2018
%o A160008 (GAP) List(List([0..15],n->Sum([0..Int(n/2)],k->(-1)^k*Factorial(n)*(8/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))),NumeratorRat); # _Muniru A Asiru_, Jul 17 2018
%Y A160008 Cf. A009969 (denominators).
%K A160008 sign,frac
%O A160008 0,2
%A A160008 _N. J. A. Sloane_, Nov 12 2009

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