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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.

%I A193975 #8 Jan 17 2014 10:12:48
%S A193975 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 A193975 100,133,168,9,26,50,80,115,154,196,240,10,29,56,90,130,175,224,276,
%U A193975 330,11,32,62,100,145,196,252,312,375,440,12,35,68,110,160,217,280
%N 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.
%C A193975 See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.
%e A193975 First six rows:
%e A193975 2
%e A193975 3...8
%e A193975 4...11...20
%e A193975 5...14...26...40
%e A193975 6...17...32...50...70
%e A193975 7...20...38...60...85...112
%t A193975 z = 11;
%t A193975 p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
%t A193975 q[n_, x_] := p[n, x];
%t A193975 p1[n_, k_] := Coefficient[p[n, x], x^k];
%t A193975 p1[n_, 0] := p[n, x] /. x -> 0;
%t A193975 d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
%t A193975 h[n_] := CoefficientList[d[n, x], {x}]
%t A193975 TableForm[Table[Reverse[h[n]], {n, 0, z}]]
%t A193975 Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193975 *)
%t A193975 TableForm[Table[h[n], {n, 0, z}]]
%t A193975 Flatten[Table[h[n], {n, -1, z}]]  (* A193976 *)
%Y A193975 Cf. A193842, A193976.
%K A193975 nonn,tabl
%O A193975 0,1
%A A193975 _Clark Kimberling_, Aug 10 2011