A160309 - OEIS

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

%S 1,22,-1438,-116204,5735020,1019546792,-32683512776,-12476450886416,

%T 165242061387152,195473234180049760,1442053974086139424,

%U -3725270373510661319872,-112443853337363708739392,83445871121227891089261184,4645331284154383230526194560

%N Numerator of Hermite(n, 11/31).

%H G. C. Greubel, <a href="/A160309/b160309.txt">Table of n, a(n) for n = 0..368</a>

%F From _G. C. Greubel_, Oct 04 2018: (Start)

%F a(n) = 31^n * Hermite(n, 11/31).

%F a(n+2) = 22*a(n+1) - 1922*(n+1)*a(n)

%F E.g.f.: exp(22*x - 961*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 22/31, -1438/961, -116204/29791, 5735020/923521, ...

%t Table[31^n*HermiteH[n, 11/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 11/31)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 04 2018

%Y Cf. A009975 (denominators).

%K sign,frac

%O 0,2

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