A375046 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) = x+2. See Comments.

3, 1, 12, 7, 1, 72, 54, 13, 1, 720, 612, 184, 23, 1, 12960, 11736, 3924, 598, 41, 1, 440640, 411984, 145152, 24256, 1992, 75, 1, 29082240, 27631584, 9992016, 1746048, 155728, 6942, 141, 1, 3780691200, 3621188160, 1326593664, 236978256, 21990688, 1058188

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
3 + x,
12 + 7 x + x^2,
72 + 54 x + 13 x^2 + x^3.
First 5 rows of array:
    3      1
   12      7     1
   72     54    13    1
  720    612   184   23   1
12960  11736  3924  598  41  1
		

Crossrefs

Cf. A000079, A139486 (column 1), A000012 (T(n,n+1)), A374848.

Programs

Mathematica

s[n_] := 2^n  x; t[n_] := x + 2;
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 *)