A193893 Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{(k+1)(n+1)*x^(n-k) : 0<=k<=n}.

1, 2, 4, 12, 28, 44, 36, 90, 150, 210, 80, 208, 360, 520, 680, 150, 400, 710, 1050, 1400, 1750, 252, 684, 1236, 1860, 2520, 3192, 3864, 392, 1078, 1974, 3010, 4130, 5292, 6468, 7644, 576, 1600, 2960, 4560, 6320, 8176, 10080, 12000, 13920, 810

Offset

0,2

Comments

See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.

Links

Table of n, a(n) for n=0..45.

Example

First six rows:
1
2....4
12...28....44
36...90....150...210
80...208...360...520....680
150..400...710...1050...1400...1760

Mathematica

z = 9;
p[n_, x_] := Sum[(k + 1) (n + 1)*x^(n - k), {k, 0, n}]
q[n_, x_] := p[n, x];
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193893 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193894 *)

Crossrefs

Cf. A193722.

Sequence in context: A148174 A232218 A292065 * A096581 A275434 A364316

Adjacent sequences: A193890 A193891 A193892 * A193894 A193895 A193896

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved