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A160259 Numerator of Hermite(n, 11/29). 1

%I #13 Mar 18 2023 16:56:55

%S 1,22,-1198,-100364,3837100,759665192,-15557376776,-8008803406736,

%T 6978879212432,107919993983713120,2268593594123893024,

%U -1765305239735329031872,-80810233952657507431232,33853095811859416015817344,2511764683469716209839300480

%N Numerator of Hermite(n, 11/29).

%H G. C. Greubel, <a href="/A160259/b160259.txt">Table of n, a(n) for n = 0..371</a>

%F From _G. C. Greubel_, Sep 26 2018: (Start)

%F a(n) = 29^n * Hermite(n, 11/29).

%F E.g.f.: exp(22*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 22/29, -1198/841, -100364/24389, 3837100/707281,...

%t Table[29^n*HermiteH[n, 11/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)

%t HermiteH[Range[0,20],11/29]//Numerator (* _Harvey P. Dale_, Mar 18 2023 *)

%o (PARI) a(n)=numerator(polhermite(n, 11/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018

%Y Cf. A009973 (denominators).

%K sign,frac

%O 0,2

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

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Last modified March 29 06:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)