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 A193975 Triangular array:  the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n+1, where p(0,x)=1. 2

%I

%S 2,3,8,4,11,20,5,14,26,40,6,17,32,50,70,7,20,38,60,85,112,8,23,44,70,

%T 100,133,168,9,26,50,80,115,154,196,240,10,29,56,90,130,175,224,276,

%U 330,11,32,62,100,145,196,252,312,375,440,12,35,68,110,160,217,280

%N Triangular array: the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n+1, where p(0,x)=1.

%C See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.

%e First six rows:

%e 2

%e 3...8

%e 4...11...20

%e 5...14...26...40

%e 6...17...32...50...70

%e 7...20...38...60...85...112

%t z = 11;

%t p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;

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

%t p1[n_, k_] := Coefficient[p[n, x], x^k];

%t p1[n_, 0] := p[n, x] /. x -> 0;

%t d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]

%t h[n_] := CoefficientList[d[n, x], {x}]

%t TableForm[Table[Reverse[h[n]], {n, 0, z}]]

%t Flatten[Table[Reverse[h[n]], {n, -1, z}]] (* A193975 *)

%t TableForm[Table[h[n], {n, 0, z}]]

%t Flatten[Table[h[n], {n, -1, z}]] (* A193976 *)

%Y Cf. A193842, A193976.

%K nonn,tabl

%O 0,1

%A _Clark Kimberling_, Aug 10 2011

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Last modified December 2 12:01 EST 2021. Contains 349440 sequences. (Running on oeis4.)