A375045 Irregular triangular array T; row n shows the coefficients of the (n-1)-st polynomial in the obverse convolution s(x)**t(x), where s(x) = 2^n and t(x) = 2x+1. See Comments.

2, 2, 6, 10, 4, 30, 62, 40, 8, 270, 618, 484, 152, 16, 4590, 11046, 9464, 3552, 576, 32, 151470, 373698, 334404, 136144, 26112, 2208, 64, 9845550, 24593310, 22483656, 9518168, 1969568, 195744, 8576, 128, 1270075950, 3192228090, 2949578244, 1272810984

Offset: 1

Author

Clark Kimberling, Sep 15 2024

Keywords

• nonn
• tabf

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences and arrays.

Examples

			First 3 polynomials in s(x)**t(x) are
2 + 2x,
6 + 10 x + 4 x^2,
30 + 62 x + 40 x^2 + 8 x^3.
First 5 rows of array:
   2      2
   6     10     4
  30     62    40     8
 270    618   484   152   16
4590  11046  9464  3552  576  32
		

Crossrefs

Cf. A000079, A028361 (column 2), A000079 (T(n,n+1)), A374848.

Programs

Mathematica

s[n_] := 2^n  x; t[n_] := 2x + 1;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[Expand[u[n]], {n, 0, 10}]
Column[Table[CoefficientList[Expand[u[n]], x], {n, 0, 10}]]   (* array *)
Flatten[Table[CoefficientList[Expand[u[n]], x], {n, 0, 10}]]  (* sequence *)