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%I #11 Sep 08 2022 08:45:44
%S 1,21,103,-12033,-357135,8768781,787702551,-1241334297,-1889772255903,
%T -36328649434875,4985785564324551,227492331940693071,
%U -13759811757404126127,-1211664945256937744643,35015649011638037564535,6468927150200228196505911,-41681870334800058325568319
%N Numerator of Hermite(n, 21/26).
%H G. C. Greubel, <a href="/A160082/b160082.txt">Table of n, a(n) for n = 0..422</a>
%F From _G. C. Greubel_, Sep 23 2018: (Start)
%F a(n) = 13^n * Hermite(n, 21/26).
%F E.g.f.: exp(21*x - 169*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(21/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 21/13, 103/169, -12033/2197, -357135/28561
%t Table[13^n*HermiteH[n, 21/26], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 21/26)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(21*x - 169*x^2))) \\ _G. C. Greubel_, Sep 23 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(21/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018
%Y Cf. A001022 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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