A375044 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 x and t(x) = x+1. See Comments.

1, 2, 1, 5, 6, 1, 10, 31, 30, 1, 19, 121, 309, 270, 1, 36, 444, 2366, 5523, 4590, 1, 69, 1632, 17018, 83601, 186849, 151470, 1, 134, 6117, 123098, 1189771, 5620914, 12296655, 9845550, 1, 263, 23403, 912191, 17069413, 159101373, 737394561, 1596114045

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
1 + 2x,
1 + 5 x + 6 x^2,
1 + 10 x + 31 x^2 + 30 x^3.
First 5 rows of array:
1    2
1    5     6
1   10    31    30
1   19   121   309    270
1   36   444  2366   5523   4590
		

Crossrefs

Cf. A000290, A028361 (T(n,n+1)), A374848.

Programs

Mathematica

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