|
|
A193897
|
|
Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{(k+1)*x^k : 0<=k<=n}.
|
|
3
|
|
|
1, 2, 1, 3, 6, 3, 4, 9, 12, 6, 5, 12, 18, 20, 10, 6, 15, 24, 30, 30, 15, 7, 18, 30, 40, 45, 42, 21, 8, 21, 36, 50, 60, 63, 56, 28, 9, 24, 42, 60, 75, 84, 84, 72, 36, 10, 27, 48, 70, 90, 105, 112, 108, 90, 45, 11, 30, 54, 80, 105, 126, 140, 144, 135, 110, 55, 12, 33
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
|
|
LINKS
|
|
|
EXAMPLE
|
1
2...1
3...6....3
4...9....12...6
5...12...18...20...10
6...15...24...30...30...15
|
|
MATHEMATICA
|
z = 12;
p[n_, x_] := (n + 1)*x^n + p[n - 1, x] (* #7 *); p[0, x_] := 1;
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}]] (* A193897 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193898 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|