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A375044
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) = 2^n x and t(x) = x+1. See Comments.
1
1, 2, 1, 5, 6, 1, 10, 31, 30, 1, 19, 121, 309, 270, 1, 36, 444, 2366, 5523, 4590, 1, 69, 1632, 17018, 83601, 186849, 151470, 1, 134, 6117, 123098, 1189771, 5620914, 12296655, 9845550, 1, 263, 23403, 912191, 17069413, 159101373, 737394561, 1596114045
OFFSET
1,2
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 + 2x,
1 + 5 x + 6 x^2,
1 + 10 x + 31 x^2 + 30 x^3.
First 5 rows of array:
1 2
1 5 6
1 10 31 30
1 19 121 309 270
1 36 444 2366 5523 4590
MATHEMATICA
s[n_] := 2^n x; t[n_] := x + 1;
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, A028361 (T(n,n+1)), A374848.
Sequence in context: A241168 A145324 A260613 * A375042 A179457 A107783
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Sep 15 2024
STATUS
approved