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A110518 Riordan array (1, x*c(3x)), c(x) the g.f. of A000108.

%I A110518 #18 Aug 30 2017 09:37:51
%S A110518 1,0,1,0,3,1,0,18,6,1,0,135,45,9,1,0,1134,378,81,12,1,0,10206,3402,
%T A110518 756,126,15,1,0,96228,32076,7290,1296,180,18,1,0,938223,312741,72171,
%U A110518 13365,2025,243,21,1,0,9382230,3127410,729729,138996,22275,2970,315,24,1,0
%N A110518 Riordan array (1, x*c(3x)), c(x) the g.f. of A000108.
%C A110518 Row sums are C(3;n), A064063. Inverse is A110517. Diagonal sums are A110525.
%H A110518 G. C. Greubel, <a href="/A110518/b110518.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A110518 Number triangle: T(0,k) = 0^k, T(n,k) = (k/n)*C(2n-k-1, n-k)*3^(n-k), n > 0, k > 0.
%F A110518 T(n,k) = A106566(n,k)*3^(n-k). - _Philippe Deléham_, Nov 08 2007
%F A110518 Triangle T(n,k), 0 <= k <= n, read by rows, given by (0, 3, 3, 3, 3, 3, 3, 3, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Sep 23 2014
%e A110518 Rows begin
%e A110518   1;
%e A110518   0,    1;
%e A110518   0,    3,    1;
%e A110518   0,   18,    6,    1;
%e A110518   0,  135,   45,    9,    1;
%e A110518   0, 1134,  378,   81,   12,    1;
%e A110518   ...
%e A110518 Production matrix begins:
%e A110518   0,   1;
%e A110518   0,   3,   1;
%e A110518   0,   9,   3,   1;
%e A110518   0,  27,   9,   3,   1;
%e A110518   0,  81,  27,   9,   3,   1;
%e A110518   0, 243,  81,  27,   9,   3,   1;
%e A110518   ... - _Philippe Deléham_, Sep 23 2014
%t A110518 T[0, 0] := 1; T[0, k_] := 0; T[n_, k_] := (k/n)*3^(n - k)*Binomial[2*n - k - 1, n - k]; Table[T[n, k], {n, 0, 20}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Aug 29 2017 *)
%o A110518 (PARI) concat([1], for(n=1,10, for(k=0,n, print1((k/n)*3^(n-k)*binomial(2*n-k-1,n-k), ", ")))) \\ _G. C. Greubel_, Aug 29 2017
%K A110518 easy,nonn,tabl
%O A110518 0,5
%A A110518 _Paul Barry_, Jul 24 2005