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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

Table of n, a(n) for n=0..67.

EXAMPLE

First six rows of A193897:

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

Cf. A193722, A193898.

Sequence in context: A125205 A125206 A221918 * A226122 A133904 A245182

Adjacent sequences:  A193894 A193895 A193896 * A193898 A193899 A193900

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2011

STATUS

approved

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Last modified October 24 08:42 EDT 2021. Contains 348217 sequences. (Running on oeis4.)