%I #22 Mar 18 2024 12:00:14
%S 1,5,-217,-3505,140017,4092925,-148955945,-6687706825,218892836705,
%T 14041864596725,-406539275359865,-36014008700873825,
%U 902137507503591505,109095368804855545325,-2292647754582021148105,-381078348283760693301625,6416919607713933301113025
%N Numerator of Hermite(n, 5/22).
%H G. C. Greubel, <a href="/A159808/b159808.txt">Table of n, a(n) for n = 0..434</a>
%F From _G. C. Greubel_, Jul 11 2018: (Start)
%F a(n) = 11^n * Hermite(n, 5/22).
%F E.g.f.: exp(5*x - 121*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 5/11, -217/121, -3505/1331, 140017/14641, ...
%t Numerator[Table[HermiteH[n, 5/22], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)
%t Table[11^n*HermiteH[n, 5/22], {n,0,30}] (* _G. C. Greubel_, Jul 11 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 5/22)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, May 21 2018
%Y Cf. A001020 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009