A159882 - OEIS

%I #15 Sep 08 2022 08:45:44

%S 1,26,-382,-64948,-476180,262479256,9343452856,-1423288542832,

%T -106203113965168,9285433263435680,1252687316025657376,

%U -65670013710482402624,-16286195340379143010112,410305415218426865451392,234668271507253831462816640,23931248973260886967214336

%N Numerator of Hermite(n, 13/23).

%H G. C. Greubel, <a href="/A159882/b159882.txt">Table of n, a(n) for n = 0..385</a>

%F From _G. C. Greubel_, Jul 16 2018: (Start)

%F a(n) = 23^n * Hermite(n, 13/23).

%F E.g.f.: exp(26*x - 529*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 26/23, -382/529, -64948/12167, -476180/279841, ...

%t Numerator[Table[HermiteH[n, 13/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 13/23], {n,0,30}] (* _G. C. Greubel_, Jul 16 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 13/23)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(26*x - 529*x^2))) \\ _G. C. Greubel_, Jul 16 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 16 2018

%Y Cf. A009967 (denominators).

%K sign,frac

%O 0,2

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