%I #15 Apr 27 2021 15:35:46

%S 1,2,8,24,84,272,920,3040,10180,33840,112968,376224,1254696,4181088,

%T 13939248,46459584,154873860,516229040,1720795880,5735921440,

%U 19119861304,63732624672,212442552528,708140901184,2360471473384,7868234639072,26227455730640

%N a(n) = Sum_{k=0..n} C(n,floor(k/2))*(-1)^k*3^(n-k).

%C Hankel transform is 4^n. Second binomial transform is A076035.

%H Vincenzo Librandi, <a href="/A133443/b133443.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = Sum_{k=0..n} A053121(n,k)*A015518(k+1) = (-1)^n*A127362(n). G.f.: (1/sqrt(1-4*x^2))*(1-x*c(x^2))/(1-3*x*c(x^2)), where c(x) is the g.f. of Catalan numbers A000108.

%F Recurrence: 3*n*a(n) = 2*(5*n-3)*a(n-1) + 4*(3*n-1)*a(n-2) - 40*(n-2)*a(n-3). - _Vaclav Kotesovec_, Oct 20 2012

%F a(n) ~ 2*10^n/3^(n+1). - _Vaclav Kotesovec_, Oct 20 2012

%t Table[Sum[Binomial[n,Floor[k/2]]*(-1)^k*3^(n-k),{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 20 2012 *)

%Y Cf. A000108, A015518, A053121, A076035, A127362.

%K nonn

%O 0,2

%A _Philippe Deléham_, Nov 26 2007, Dec 07 2007

%E More terms from _Vincenzo Librandi_, May 25 2013