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A375045
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 and t(x) = 2x+1. See Comments.
1
2, 2, 6, 10, 4, 30, 62, 40, 8, 270, 618, 484, 152, 16, 4590, 11046, 9464, 3552, 576, 32, 151470, 373698, 334404, 136144, 26112, 2208, 64, 9845550, 24593310, 22483656, 9518168, 1969568, 195744, 8576, 128, 1270075950, 3192228090, 2949578244, 1272810984
OFFSET
1,1
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
2 + 2x,
6 + 10 x + 4 x^2,
30 + 62 x + 40 x^2 + 8 x^3.
First 5 rows of array:
2 2
6 10 4
30 62 40 8
270 618 484 152 16
4590 11046 9464 3552 576 32
MATHEMATICA
s[n_] := 2^n x; t[n_] := 2x + 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. A000079, A028361 (column 2), A000079 (T(n,n+1)), A374848.
Sequence in context: A327485 A207975 A321623 * A077063 A081728 A197218
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Sep 15 2024
STATUS
approved