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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

%I

%S 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,

%T 21,8,21,36,50,60,63,56,28,9,24,42,60,75,84,84,72,36,10,27,48,70,90,

%U 105,112,108,90,45,11,30,54,80,105,126,140,144,135,110,55,12,33

%N Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{(k+1)*x^k : 0<=k<=n}.

%C See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.

%e First six rows of A193897:

%e 1

%e 2...1

%e 3...6....3

%e 4...9....12...6

%e 5...12...18...20...10

%e 6...15...24...30...30...15

%t z = 12;

%t p[n_, x_] := (n + 1)*x^n + p[n - 1, x] (* #7 *); p[0, x_] := 1;

%t q[n_, x_] := p[n, x];

%t t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;

%t w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

%t g[n_] := CoefficientList[w[n, x], {x}]

%t TableForm[Table[Reverse[g[n]], {n, -1, z}]]

%t Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193897 *)

%t TableForm[Table[g[n], {n, -1, z}]]

%t Flatten[Table[g[n], {n, -1, z}]] (* A193898 *)

%Y Cf. A193722, A193898.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 08 2011

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)