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

0,2

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.

Links

Table of n, a(n) for n=0..24.

Formula

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

Example

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; ...

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 *)

Prog

(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)}

Crossrefs

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

Sequence in context: A292158 A303729 A296544 * A062743 A370825 A009084

Adjacent sequences: A136632 A136633 A136634 * A136636 A136637 A136638

Keyword

nonn,tabl

Author

Vladeta Jovovic and Paul D. Hanna, Jan 15 2008

Status

approved