A386825 Triangle read by rows: T(n,k) = 3^(n-k)*C(2*n,n-k).

1, 6, 1, 54, 12, 1, 540, 135, 18, 1, 5670, 1512, 252, 24, 1, 61236, 17010, 3240, 405, 30, 1, 673596, 192456, 40095, 5940, 594, 36, 1, 7505784, 2189187, 486486, 81081, 9828, 819, 42, 1, 84440070, 25019280, 5837832, 1061424, 147420, 15120, 1080, 48, 1, 956987460, 287096238

Offset

0,2

Comments

Row sums are A386826.

Links

Table of n, a(n) for n=0..46.

Formula

T(n,k) = 3^(n-k)*A094527(n,k).

Example

Triangle begins:
        1;
        6,       1;
       54,      12,      1;
      540,     135,     18,     1;
     5670,    1512,    252,    24,    1;
    61236,   17010,   3240,   405,   30,   1;
   673596,  192456,  40095,  5940,  594,  36,  1;
  7505784, 2189187, 486486, 81081, 9828, 819, 42, 1;
  ...

Mathematica

Flatten[Table[3^(n-k) Binomial[2n, n-k], {n, 0, 9}, {k, 0, n}]]

Crossrefs

Cf. A094527, A128417, A386826.

Sequence in context: A113387 A290316 A090435 * A136237 A308281 A347211

Adjacent sequences: A386822 A386823 A386824 * A386826 A386827 A386828

Keyword

nonn,tabl

Author

Enrique Navarrete, Aug 04 2025

Status

approved