A193895 Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{(k+1)*x^(n-k) : 0<=k<=n} and q(n,x)=sum{(k+1)*x^k : 0<=k<=n}.

1, 2, 1, 6, 6, 3, 12, 15, 12, 6, 20, 28, 27, 20, 10, 30, 45, 48, 42, 30, 15, 42, 66, 75, 72, 60, 42, 21, 56, 91, 108, 110, 100, 81, 56, 28, 72, 120, 147, 156, 150, 132, 105, 72, 36, 90, 153, 192, 210, 210, 195, 168, 132, 90, 45, 110, 190, 243, 272, 280, 270

Offset

0,2

Comments

See A193722 for the definition of fusion of P by Q (two sequences of polynomials or triangular arrays).

...

First six rows of P, the coefficients of (p(n,x)):

1

1...2

1...2...3

1...2...3...4

1...2...3...4...5

...

First six rows of Q, the coefficients of (q(n,x)):

1

2...1

3...2...1

4...3...2...1

5...4..3...2..1

Links

Table of n, a(n) for n=0..60.

Example

First six rows of A193895:
1
2....1
6....6....3
12...15...12...6
20...28...27...20...10
30...45...48...42...30...15

Mathematica

z = 9;
p[n_, x_] := x*p[n - 1, x] + n + 1 (* #6 *)  ; p[0, x_] := 1;
q[n_, x_] := (n + 1)*x^n + q[n - 1, x] (* #7 *); q[0, x_] := 1;
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}]]  (* A193895 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193896 *)

Crossrefs

A193722, A193896.

Sequence in context: A260885 A075181 A052121 * A193561 A328349 A117965

Adjacent sequences: A193892 A193893 A193894 * A193896 A193897 A193898

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved