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A375041
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) = n^2 x and t(x) = x+1. See Comments.
3
1, 1, 1, 3, 2, 1, 8, 17, 10, 1, 18, 97, 180, 100, 1, 35, 403, 1829, 3160, 1700, 1, 61, 1313, 12307, 50714, 83860, 44200, 1, 98, 3570, 60888, 506073, 1960278, 3147020, 1635400, 1, 148, 8470, 239388, 3550473, 27263928, 101160920, 158986400, 81770000, 1, 213
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
1 + x,
1 + 3 x + 2 x^2,
1 + 8 x + 17 x^2 + 10 x^3.
First 5 rows of array:
1 1
1 3 2
1 8 17 10
1 18 97 180 100
1 35 4034 1829 3160 1700
MATHEMATICA
s[n_] := n^2 x; t[n_] := 1 + x;
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. A000290, A081489 (column 2), A101686 (T(n,n+1)), A374848, A375042, A375043.
Sequence in context: A203992 A204019 A196846 * A101413 A101908 A290310
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Sep 11 2024
STATUS
approved