A375046 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) = x+2. See Comments.

3, 1, 12, 7, 1, 72, 54, 13, 1, 720, 612, 184, 23, 1, 12960, 11736, 3924, 598, 41, 1, 440640, 411984, 145152, 24256, 1992, 75, 1, 29082240, 27631584, 9992016, 1746048, 155728, 6942, 141, 1, 3780691200, 3621188160, 1326593664, 236978256, 21990688, 1058188

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..41.

Example

First 3 polynomials in s(x)**t(x) are
3 + x,
12 + 7 x + x^2,
72 + 54 x + 13 x^2 + x^3.
First 5 rows of array:
    3      1
   12      7     1
   72     54    13    1
  720    612   184   23   1
12960  11736  3924  598  41  1

Mathematica

s[n_] := 2^n  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. A000079, A139486 (column 1), A000012 (T(n,n+1)), A374848.

Sequence in context: A133366 A049458 A143492 * A243662 A062139 A156366

Adjacent sequences: A375043 A375044 A375045 * A375047 A375048 A375049

Keyword

nonn,tabf

Author

Clark Kimberling, Sep 15 2024

Status

approved