A375048 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) = x+F(n) and t(x) = F(n), where F(n) = n-th Fibonacci number (A000045). See Comments.

0, 1, 1, 2, 1, 2, 5, 4, 1, 16, 32, 24, 8, 1, 162, 297, 216, 78, 14, 1, 3600, 5640, 3649, 1248, 238, 24, 1, 147456, 196608, 110848, 34240, 6256, 676, 40, 1, 12320100, 13667940, 6521589, 1746426, 286843, 29568, 1867, 66, 1, 2058386904, 1878686460, 746158770

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
0 + x,
1 + 2 x + x^2,
2 + 4 x + 4 x^2 + x^3.
First 5 rows of array:
  0    1
  1    2    1
  2    5    4   1
 16   32   24   8   1
162  297  216  78  14  1
		

Crossrefs

Cf. A000045, A019274 (T(n,n)), A374848, A375047, A375049.

Programs

Mathematica

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