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.

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.

Links

Table of n, a(n) for n=1..46.

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

Adjacent sequences: A375038 A375039 A375040 * A375042 A375043 A375044

Keyword

nonn,tabf

Author

Clark Kimberling, Sep 11 2024

Status

approved