A152556 - OEIS

%I #12 Sep 08 2022 08:45:39

%S 1,2,2,16,20,288,392,8192,11664,320000,468512,15925248,23762752,

%T 963780608,1458000000,68719476736,105046700288,5642219814912,

%U 8695584276992,524288000000000,813342767698944,54394721876836352,84841494965553152,6232805962420322304

%N a(n) = 2*(2*n+2)^floor((n-1)/2).

%C Compare to row sums of triangle A152555: 2*(2n+2)^(n-1).

%C Triangle A152555 lists coefficients in a q-analog of the function LambertW(-2x)/(-2x).

%H G. C. Greubel, <a href="/A152556/b152556.txt">Table of n, a(n) for n = 0..640</a>

%F a(n) = Sum_{k=0..n(n-1)/2} A152555(n,k)*(-1)^k.

%t Table[2(2n+2)^Floor[(n-1)/2],{n,0,30}] (* _Harvey P. Dale_, Nov 13 2012 *)

%o (PARI) a(n)=2*(2*n+2)^((n-1)\2)

%o (Magma) [2*(2*n+2)^(Floor((n-1)/2)): n in [0..30]]; // _G. C. Greubel_, Nov 17 2017

%Y Cf. A152555, A152557(q=2), A152558 (q=3) A152559.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 07 2008