cp's OEIS Frontend

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.

%I A375047 #5 Sep 20 2024 06:08:55
%S A375047 1,1,2,3,1,4,8,5,1,12,28,23,8,1,48,124,120,55,12,1,288,792,844,450,
%T A375047 127,18,1,2592,7416,8388,4894,1593,289,27,1,36288,106416,124848,76904,
%U A375047 27196,5639,667,41,1,798336,2377440,2853072,1816736,675216,151254,20313
%N 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.
%C A375047 See A374848 for the definition of obverse convolution and a guide to related sequences and arrays.
%e A375047 First 3 polynomials in s(x)**t(x) are
%e A375047 1 + x,
%e A375047 2 + 3 x + x^2,
%e A375047 4 + 8 x + 5 x^2 + x^3.
%e A375047 First 5 rows of array:
%e A375047  1    1
%e A375047  2    3    1
%e A375047  4    8    5   1
%e A375047 12   28   23   8   1
%e A375047 48  124  120  55  12  1
%t A375047 s[n_] := x + 1; t[n_] := Fibonacci[n];
%t A375047 u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
%t A375047 Table[Expand[u[n]], {n, 0, 10}]
%t A375047 Column[Table[CoefficientList[Expand[u[n]], x], {n, 0, 10}]]   (* array *)
%t A375047 Flatten[Table[CoefficientList[Expand[u[n]], x], {n, 0, 10}]]  (* sequence *)
%Y A375047 Cf. A000045, A232896 (T(n,n)), A374848, A375048, A375049.
%K A375047 nonn,tabf
%O A375047 1,3
%A A375047 _Clark Kimberling_, Sep 15 2024