A193977 Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=sum{(k+1)*x^k ; 0<=k<=n}.

2, 6, 5, 12, 14, 9, 20, 27, 24, 14, 30, 44, 45, 36, 20, 42, 65, 72, 66, 50, 27, 56, 90, 105, 104, 90, 66, 35, 72, 119, 144, 150, 140, 117, 84, 44, 90, 152, 189, 204, 200, 180, 147, 104, 54, 110, 189, 240, 266, 270, 255, 224, 180, 126, 65, 132, 230, 297, 336

Offset: 0

Author

Clark Kimberling, Aug 10 2011

Keywords

• nonn
• tabl

Comments

See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.

Examples

			First six rows:
2
6....5
12...14...9
20...27...24...14
30...44...45...36...20
42...65...72...66...50...27
		

Crossrefs

Cf. A193842, A193978.

Programs

Mathematica

z = 11;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
q[n_, x_] := Sum[(k + 1)*x^k, {k, 0, n}]
p1[n_, k_] := Coefficient[p[n, x], x^k];
p1[n_, 0] := p[n, x] /. x -> 0;
d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
h[n_] := CoefficientList[d[n, x], {x}]
TableForm[Table[Reverse[h[n]], {n, 0, z}]]
Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193977 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A193978 *)