A160236 - OEIS

%I #13 Sep 08 2022 08:45:45

%S 1,10,-1582,-49460,7488172,407648600,-58899040520,-4702980076400,

%T 646447502318480,69747774931223200,-9088444540784918240,

%U -1264042019751023406400,155513980696092323212480,27068563933615579666902400,-3129783062564598942695063680

%N Numerator of Hermite(n, 5/29).

%H G. C. Greubel, <a href="/A160236/b160236.txt">Table of n, a(n) for n = 0..372</a>

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

%F a(n) = 29^n * Hermite(n, 5/29).

%F E.g.f.: exp(10*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 10/29, -1582/841, -49460/24389, 7488172/707281

%t Numerator[HermiteH[Range[0,20],5/29]] (* _Harvey P. Dale_, Mar 10 2013 *)

%t Table[29^n*HermiteH[n, 5/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 5/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(10*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/29)^(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