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%I #10 May 04 2013 06:39:27
%S 1,4,12,35,101,291,839,2423,7011,20326,59038,171777,500603,1461032,
%T 4269828,12493857,36599403,107325540,315027276,925501857,2721208599,
%U 8007114171,23577440439,69470880381,204821487269,604223501426,1783419354954,5266582196407,15560042628205
%N Inverse binomial transform of A002054.
%H Vincenzo Librandi, <a href="/A035045/b035045.txt">Table of n, a(n) for n = 0..1000</a>
%F Recurrence: (n+3)*(3*n-1)*a(n) = (6*n^2+19*n+7)*a(n-1) + 3*(n-1)*(3*n+2)*a(n-2). - _Vaclav Kotesovec_, Oct 08 2012
%F a(n) ~ 4*3^(n+1/2)/sqrt(Pi*n). - _Vaclav Kotesovec_, Oct 08 2012
%t Table[Sum[(-1)^(n-k)*Binomial[n,k]*Binomial[2k+3,k],{k,0,n}],{n,0,22}] (* _Vaclav Kotesovec_, Oct 08 2012 *)
%o (PARI) a(n)=sum(k=0,n,(-1)^(n-k)*binomial(n,k)*binomial(2*k+3,k) ); \\ _Joerg Arndt_, May 04 2013
%Y Cf. A005774.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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