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%I #11 Jun 13 2015 09:39:28
%S 1,3,2,36,30,6,2925,2448,660,56,1663740,1265004,353430,42504,1820,
%T 6774333588,4368213360,1114691760,139915440,8561520,201376,
%U 204208594169580,106458751541142,23004238451040,2630276490960
%N Triangle, read by rows, where T(n,k) = C(n,k) * C(2^k*3^(n-k), n) for n>=k>=0.
%C Main diagonal is A014070(n) = C(2^n,n).
%C Column 0 is A136393(n) = C(3^n,n).
%C Row sums form A136637.
%C Antidiagonal sums form A136638.
%F G.f.: A(x,y) = Sum_{n>=0} log(1 + 3^n*x + 2^n*x*y)^n / n!.
%e Triangle begins:
%e 1;
%e 3, 2;
%e 36, 30, 6;
%e 2925, 2448, 660, 56;
%e 1663740, 1265004, 353430, 42504, 1820;
%e 6774333588, 4368213360, 1114691760, 139915440, 8561520, 201376;
%e 204208594169580, 106458751541142, 23004238451040, 2630276490960, 167150463480, 5562289824, 74974368; ...
%t Flatten[Table[Binomial[n,k]Binomial[2^k 3^(n-k),n],{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Dec 13 2012 *)
%o (PARI) {T(n,k)=binomial(n,k)*binomial(2^k*3^(n-k),n)}
%o (PARI) /* Using g.f.: */ {T(n,k)=polcoeff(polcoeff(sum(i=0,n,log(1+3^i*x+2^i*x*y)^i/i!),n,x),k,y)}
%Y Cf. A014070 (main diagonal), A136393 (column 0), A136636 (column 1), A136637 (row sums), A136638 (antidiagonal sums).
%K nonn,tabl
%O 0,2
%A _Vladeta Jovovic_ and _Paul D. Hanna_, Jan 15 2008
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