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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.

%I A375048 #4 Sep 20 2024 06:09:06
%S A375048 0,1,1,2,1,2,5,4,1,16,32,24,8,1,162,297,216,78,14,1,3600,5640,3649,
%T A375048 1248,238,24,1,147456,196608,110848,34240,6256,676,40,1,12320100,
%U A375048 13667940,6521589,1746426,286843,29568,1867,66,1,2058386904,1878686460,746158770
%N 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.
%C A375048 See A374848 for the definition of obverse convolution and a guide to related sequences and arrays.
%e A375048 First 3 polynomials in s(x)**t(x) are
%e A375048 0 + x,
%e A375048 1 + 2 x + x^2,
%e A375048 2 + 4 x + 4 x^2 + x^3.
%e A375048 First 5 rows of array:
%e A375048   0    1
%e A375048   1    2    1
%e A375048   2    5    4   1
%e A375048  16   32   24   8   1
%e A375048 162  297  216  78  14  1
%t A375048 s[n_] := x + Fibonacci[n]; t[n_] := Fibonacci[n];
%t A375048 u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
%t A375048 Table[Expand[u[n]], {n, 0, 10}]
%t A375048 Column[Table[CoefficientList[Expand[u[n]], x], {n, 0, 10}]]   (* array *)
%t A375048 Flatten[Table[CoefficientList[Expand[u[n]], x], {n, 0, 10}]]  (* sequence *)
%Y A375048 Cf. A000045, A019274 (T(n,n)), A374848, A375047, A375049.
%K A375048 nonn,tabf
%O A375048 1,4
%A A375048 _Clark Kimberling_, Sep 15 2024