A160283 - OEIS

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

%S 1,42,82,-137844,-6203220,666879192,80178006264,-3362668542576,

%T -1085247924540528,-332344921799520,16414524594978933024,

%U 695000074573783113408,-274511530924201328046912,-25557365804013694138997376,4929059771420011085235888000

%N Numerator of Hermite(n, 21/29).

%H G. C. Greubel, <a href="/A160283/b160283.txt">Table of n, a(n) for n = 0..371</a>

%F From _G. C. Greubel_, Oct 03 2018: (Start)

%F a(n) = 29^n * Hermite(n, 21/29).

%F E.g.f.: exp(42*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(42/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 42/29, 82/841, -137844/24389, -6203220/707281, ...

%t Table[29^n*HermiteH[n, 21/29], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 21/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(42*x - 841*x^2))) \\ _G. C. Greubel_, Oct 03 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(42/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 03 2018

%Y Cf. A009973 (denominators).

%K sign,frac

%O 0,2

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