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A193963 Triangular array:  the self-fusion of (p(n,x)), where p(n,x)=sum{((k+1)^2)*x^k  :  0<=k<=n}. 2

%I

%S 1,4,1,9,20,5,16,45,56,14,25,80,126,120,30,36,125,224,270,220,55,49,

%T 180,350,480,495,364,91,64,245,504,750,880,819,560,140,81,320,686,

%U 1080,1375,1456,1260,816,204,100,405,896,1470,1980,2275,2240,1836,1140

%N Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{((k+1)^2)*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:

%e 1

%e 4....1

%e 9....20....5

%e 16...45....56....14

%e 25...80....126...120...30

%e 36...125...224...270...220...55

%t z = 12;

%t p[n_, x_] := Sum[((k + 1)^2)*x^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}]] (* A193963 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193964 *)

%Y Cf. A193722, A193964.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 10 2011

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Last modified January 24 09:20 EST 2022. Contains 350534 sequences. (Running on oeis4.)