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

1,4

Comments

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

Links

Table of n, a(n) for n=1..47.

Example

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

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 *)

Crossrefs

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

Sequence in context: A121435 A137156 A136457 * A209133 A078016 A078046

Adjacent sequences: A375045 A375046 A375047 * A375049 A375050 A375051

Keyword

nonn,tabf

Author

Clark Kimberling, Sep 15 2024

Status

approved