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A375049
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) = x+F(n), and F(n) = n-th Fibonacci number (A000045). See Comments.
3
0, 2, 1, 4, 4, 2, 10, 16, 8, 16, 64, 96, 64, 16, 162, 594, 864, 624, 224, 32, 3600, 11280, 14596, 9984, 3808, 768, 64, 147456, 393216, 443392, 273920, 100096, 21632, 2560, 128, 12320100, 27335880, 26086356, 13971408, 4589488, 946176, 119488, 8448, 256
OFFSET
1,2
COMMENTS
See A374848 for the definition of obverse convolution and a guide to related sequences and arrays. If n is odd, then the polynomial u(n) is a square. Every T(n,k) except T(2,1) is even.
EXAMPLE
First 3 polynomials in s(x)**t(x) are
0 + 2x,
1 + 4 x + 4x^2,
2 + 10 x + 16 x^2 + 8 x^3.
First 5 rows of array:
0 2
1 4 4
2 10 16 8
16 64 96 64 16
162 594 864 624 224 32
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, A000079 (T(n,n+1)), A374848, A375047, A375048.
Sequence in context: A051289 A134308 A090802 * A129159 A095830 A193915
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Jul 31 2024
STATUS
approved