login
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.
3
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.
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
Sequence in context: A121435 A137156 A136457 * A209133 A078016 A078046
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Sep 15 2024
STATUS
approved