A136635 Triangle, read by rows, where T(n,k) = C(n,k) * C(2^k*3^(n-k), n) for n>=k>=0.

1, 3, 2, 36, 30, 6, 2925, 2448, 660, 56, 1663740, 1265004, 353430, 42504, 1820, 6774333588, 4368213360, 1114691760, 139915440, 8561520, 201376, 204208594169580, 106458751541142, 23004238451040, 2630276490960

Offset: 0

Author

Vladeta Jovovic and Paul D. Hanna, Jan 15 2008

Keywords

• nonn
• tabl

Comments

Main diagonal is A014070(n) = C(2^n,n).

Column 0 is A136393(n) = C(3^n,n).

Row sums form A136637.

Antidiagonal sums form A136638.

Examples

			Triangle begins:
1;
3, 2;
36, 30, 6;
2925, 2448, 660, 56;
1663740, 1265004, 353430, 42504, 1820;
6774333588, 4368213360, 1114691760, 139915440, 8561520, 201376;
204208594169580, 106458751541142, 23004238451040, 2630276490960, 167150463480, 5562289824, 74974368; ...
		

Crossrefs

Cf. A014070 (main diagonal), A136393 (column 0), A136636 (column 1), A136637 (row sums), A136638 (antidiagonal sums).

Programs

Mathematica

Flatten[Table[Binomial[n,k]Binomial[2^k 3^(n-k),n],{n,0,10},{k,0,n}]] (* Harvey P. Dale, Dec 13 2012 *)

PARI

{T(n,k)=binomial(n,k)*binomial(2^k*3^(n-k),n)}

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)}

Formula

G.f.: A(x,y) = Sum_{n>=0} log(1 + 3^n*x + 2^n*x*y)^n / n!.