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A160290 Numerator of Hermite(n, 28/29). 1

%I #16 Sep 08 2022 08:45:45

%S 1,56,1454,-106960,-13326644,-26665184,110583825736,6461799278144,

%T -940153204639600,-139598550546523264,6414520381228962016,

%U 2707260761541343173376,32925146552816962489024,-52799543003992720712035840,-3676715662747488061659005824

%N Numerator of Hermite(n, 28/29).

%H G. C. Greubel, <a href="/A160290/b160290.txt">Table of n, a(n) for n = 0..372</a>

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

%F a(n) = 29^n * Hermite(n, 28/29).

%F E.g.f.: exp(56*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(56/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 56/29, 1454/841, -106960/24389, -13326644/707281, ...

%t Table[29^n*HermiteH[n, 28/29], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 28/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(56*x - 841*x^2))) \\ _G. C. Greubel_, Oct 03 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(56/29)^(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

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)