A375043 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) = n^2 x and t(x) = x+2. See Comments.

2, 1, 4, 6, 2, 8, 32, 34, 10, 16, 144, 388, 360, 100, 32, 560, 3224, 7316, 6320, 1700, 64, 1952, 21008, 98456, 202856, 167720, 44200, 128, 6272, 114240, 974208, 4048584, 7841112, 6294040, 1635400, 256, 18944, 542080, 7660416, 56807568, 218111424, 404643680

Offset: 1

Author

Clark Kimberling, Sep 14 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 + x,
4 + 6 x + 2 x^2,
8 + 32 x + 34 x^2 + 10 x^3.
First 5 rows of array:
 2    1
 4    6     2
 8   32    34    10
16  144   388   360   100
32  560  3224  7316  6320  1700
		

Crossrefs

Cf. A000290, A101686 (T(n,n+1)), A374848, A375041, A375042.

Programs

Mathematica

s[n_] := n^2  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 *)