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A193893 Triangular array:  the self-fusion of (p(n,x)), where p(n,x)=sum{(k+1)(n+1)*x^(n-k) : 0<=k<=n}. 2

%I

%S 1,2,4,12,28,44,36,90,150,210,80,208,360,520,680,150,400,710,1050,

%T 1400,1750,252,684,1236,1860,2520,3192,3864,392,1078,1974,3010,4130,

%U 5292,6468,7644,576,1600,2960,4560,6320,8176,10080,12000,13920,810

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

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

%e First six rows:

%e 1

%e 2....4

%e 12...28....44

%e 36...90....150...210

%e 80...208...360...520....680

%e 150..400...710...1050...1400...1760

%t z = 9;

%t p[n_, x_] := Sum[(k + 1) (n + 1)*x^(n - k), {k, 0, n}]

%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}]] (* A193893 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193894 *)

%Y Cf. A193722.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 08 2011

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Last modified October 16 03:52 EDT 2021. Contains 348035 sequences. (Running on oeis4.)