A159763 - OEIS

%I #24 Mar 18 2024 12:00:24

%S 1,32,142,-51904,-2036660,117944192,12755884744,-215972352256,

%T -85665947681648,-1217409408294400,641059191631501024,

%U 31251445113364640768,-5219510033581154430272,-497789616154448299657216,43917634328099171108467840,7552070478774301079638274048

%N Numerator of Hermite(n, 16/21).

%H Robert Israel, <a href="/A159763/b159763.txt">Table of n, a(n) for n = 0..391</a>

%F From _Robert Israel_, Jan 02 2018: (Start)

%F a(n) = 21^n * Hermite(n,16/21).

%F E.g.f.: exp(32*x-441*x^2).

%F a(n+2) = 32*a(n+1) - 882*(n+1)*a(n). (End)

%p seq(21^n*orthopoly[H](n,16/21), n=0..50); # _Robert Israel_, Jan 02 2018

%t Numerator[Table[HermiteH[n, 16/21], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)

%o (PARI) a(n)=numerator(polhermite(n, 16/21)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, May 21 2018

%Y Cf. A009965 (denominators).

%K sign,frac

%O 0,2

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