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A375042
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) = 2x+1. See Comments.
3
1, 2, 1, 5, 6, 1, 11, 36, 36, 1, 22, 157, 432, 396, 1, 40, 553, 3258, 8172, 7128, 1, 67, 1633, 18189, 96138, 227772, 192456, 1, 105, 4179, 80243, 787320, 3881016, 8847792, 7313328, 1, 156, 9534, 293372, 4879713, 44034336, 206779608, 458550720, 372979728, 1
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 + 11 x + 36 x^2 + 36 x^3.
First 5 rows of array:
1 2
1 5 6
1 11 36 36
1 22 157 432 396
1 40 553 3258 8172 7128
MATHEMATICA
s[n_] := n^2 x; t[n_] := 1 + 2 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, A277355 ((1/2)T(n,n+1)), A374848, A375041, A375043.
Sequence in context: A145324 A260613 A375044 * A179457 A107783 A047887
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Sep 11 2024
STATUS
approved