%I #8 Nov 04 2013 21:38:02
%S 1,4,14,46,150,494,1652,5618,19430,68302,243804,882578,3235596,
%T 11994922,44899568,169466426,644127110,2462746382,9462555788,
%U 36507525266,141333313220,548718227642,2135480023328,8327573906426,32530033219580
%N 3^n-1+C(2n,n).
%C Binomial transform of A081669
%F a(n)=A000984(n)+2*A003462(n) E.g.f. exp(3x)-exp(x)+exp(2x)BesselI_0(2x).
%F Conjecture: n*(3*n^2-17*n+26)*a(n) +2*(-12*n^3+71*n^2-131*n+60)*a(n-1) +(57*n^3-347*n^2+710*n-480)*a(n-2) -6*(2*n-5)*(3*n^2-11*n+12)*a(n-3)=0. - _R. J. Mathar_, Nov 12 2012
%e a(6) = 1652; 3^6 - 1 + binomial(12,6) = 728 + 924 = 1652.
%p A081670:=n->3^n-1+binomial(2*n,n); seq(A081670(k), k=0..50); # _Wesley Ivan Hurt_, Nov 04 2013
%t Table[3^n - 1 + Binomial[2 n, n], {n, 0, 50}] (* _Wesley Ivan Hurt_, Nov 04 2013 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 28 2003