A193961 Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{((k+1)^2)*x^(n-k) : 0<=k<=n}.

1, 1, 4, 4, 17, 40, 9, 40, 98, 184, 16, 73, 184, 354, 584, 25, 116, 298, 584, 979, 1484, 36, 169, 440, 874, 1484, 2275, 3248, 49, 232, 610, 1224, 2099, 3248, 4676, 6384, 64, 305, 808, 1634, 2824, 4403, 6384, 8772, 11568, 81, 388, 1034, 2104, 3659

Offset

0,3

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..49.

Example

First six rows:
1
1....4
4....17....40
9....40....98....184
16...73....184...354...584
25...116...298...584...979...1484

Mathematica

z = 12;
p[n_, x_] := Sum[((k + 1)^2)*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}]]  (* A193961 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193962 *)

Crossrefs

Cf. A193722, A193962.

Sequence in context: A117787 A113727 A214141 * A368197 A205110 A116561

Adjacent sequences: A193958 A193959 A193960 * A193962 A193963 A193964

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved