A013623 Triangle of coefficients in expansion of (2 + 7*x)^n.

1, 2, 7, 4, 28, 49, 8, 84, 294, 343, 16, 224, 1176, 2744, 2401, 32, 560, 3920, 13720, 24010, 16807, 64, 1344, 11760, 54880, 144060, 201684, 117649, 128, 3136, 32928, 192080, 672280, 1411788, 1647086, 823543, 256, 7168, 87808, 614656, 2689120, 7529536, 13176688, 13176688, 5764801

Offset

0,2

Links

Table of n, a(n) for n=0..44.

Formula

G.f.: 1/(1 - x*(2 + 7*y)).

Example

The triangle begins as:
   1;
   2,   7;
   4,  28,   49;
   8,  84,  294,   343;
  16, 224, 1176,  2744,  2401;
  32, 560, 3920, 13720, 24010, 16807;
  ...

Mathematica

row[n_] := Table[SeriesCoefficient[1/(1 - x*(2 + 7*y)), {x, 0, i}, {y, 0, j}], {i, n, n}, {j, 0, n}]; Flatten[Array[row, 9, 0]] (* Stefano Spezia, Aug 19 2025 *)

Crossrefs

Cf. A000079 (1st column), A000420 (diagonal), A001019 (row sums).

Sequence in context: A054787 A190716 A303384 * A345273 A348145 A210421

Adjacent sequences: A013620 A013621 A013622 * A013624 A013625 A013626

Keyword

tabl,nonn,easy

Author

N. J. A. Sloane

Status

approved