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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}. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 A117965 A111646

Adjacent sequences:  A193892 A193893 A193894 * A193896 A193897 A193898

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2011

STATUS

approved

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Last modified March 26 12:27 EDT 2019. Contains 321497 sequences. (Running on oeis4.)