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Numerator of Hermite(n, 1/22).
1

%I #24 Mar 18 2024 12:03:09

%S 1,1,-241,-725,174241,876041,-209955569,-1481967101,354182766785,

%T 3223271074321,-768186794983409,-8568502794840229,2036344745450994529,

%U 26919276861667019545,-6379421292327161768689,-97581931299655023987149,23059717359847942196353921

%N Numerator of Hermite(n, 1/22).

%H G. C. Greubel, <a href="/A159806/b159806.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, 1/22).

%F E.g.f.: exp(x - 121*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerator of 1, 1/11, -241/121, -725/1331, 174241/14641, ...

%t Numerator[Table[HermiteH[n, 1/22], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)

%t Table[11^n*HermiteH[n, 1/22], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 1/22)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/11)^(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 0,3

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