A375047 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+1 and t(x) = F(n) = n-th Fibonacci number. See Comments.

1, 1, 2, 3, 1, 4, 8, 5, 1, 12, 28, 23, 8, 1, 48, 124, 120, 55, 12, 1, 288, 792, 844, 450, 127, 18, 1, 2592, 7416, 8388, 4894, 1593, 289, 27, 1, 36288, 106416, 124848, 76904, 27196, 5639, 667, 41, 1, 798336, 2377440, 2853072, 1816736, 675216, 151254, 20313

Offset

1,3

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..51.

Example

First 3 polynomials in s(x)**t(x) are
1 + x,
2 + 3 x + x^2,
4 + 8 x + 5 x^2 + x^3.
First 5 rows of array:
 1    1
 2    3    1
 4    8    5   1
12   28   23   8   1
48  124  120  55  12  1

Mathematica

s[n_] := x + 1; 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, A232896 (T(n,n)), A374848, A375048, A375049.

Sequence in context: A321621 A321629 A353594 * A075297 A057597 A226392

Adjacent sequences: A375044 A375045 A375046 * A375048 A375049 A375050

Keyword

nonn,tabf

Author

Clark Kimberling, Sep 15 2024

Status

approved