A375043 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+2. See Comments.

2, 1, 4, 6, 2, 8, 32, 34, 10, 16, 144, 388, 360, 100, 32, 560, 3224, 7316, 6320, 1700, 64, 1952, 21008, 98456, 202856, 167720, 44200, 128, 6272, 114240, 974208, 4048584, 7841112, 6294040, 1635400, 256, 18944, 542080, 7660416, 56807568, 218111424, 404643680

Offset

1,1

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences and arrays.

Links

Table of n, a(n) for n=1..42.

Example

First 3 polynomials in s(x)**t(x) are
2 + x,
4 + 6 x + 2 x^2,
8 + 32 x + 34 x^2 + 10 x^3.
First 5 rows of array:
 2    1
 4    6     2
 8   32    34    10
16  144   388   360   100
32  560  3224  7316  6320  1700

Mathematica

s[n_] := n^2  x; t[n_] := x + 2;
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, A101686 (T(n,n+1)), A374848, A375041, A375042.

Sequence in context: A323286 A193818 A127535 * A285491 A257640 A262930

Adjacent sequences: A375040 A375041 A375042 * A375044 A375045 A375046

Keyword

nonn,tabf

Author

Clark Kimberling, Sep 14 2024

Status

approved