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A193979 Triangular array: the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n, with p(0,x)=1.

%I A193979 #8 Jan 17 2014 10:13:16
%S A193979 1,2,3,3,5,9,4,7,13,21,5,9,17,28,41,6,11,21,35,52,71,7,13,25,42,63,87,
%T A193979 113,8,15,29,49,74,103,135,169,9,17,33,56,85,119,157,198,241,10,19,37,
%U A193979 63,96,135,179,227,278,331,11,21,41,70,107,151,201,256,315,377
%N A193979 Triangular array:  the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n, with p(0,x)=1.
%C A193979 See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.
%e A193979 First six rows:
%e A193979 1
%e A193979 2...3
%e A193979 3...5...9
%e A193979 4...7...13....21
%e A193979 5...9...17....28...41
%e A193979 6...11...21...35...52...71
%t A193979 z = 11;
%t A193979 p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n;
%t A193979 q[n_, x_] := p[n, x];
%t A193979 p1[n_, k_] := Coefficient[p[n, x], x^k];
%t A193979 p1[n_, 0] := p[n, x] /. x -> 0;
%t A193979 d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
%t A193979 h[n_] := CoefficientList[d[n, x], {x}]
%t A193979 TableForm[Table[Reverse[h[n]], {n, 0, z}]]
%t A193979 Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193979 *)
%t A193979 TableForm[Table[h[n], {n, 0, z}]]
%t A193979 Flatten[Table[h[n], {n, -1, z}]]  (* A193980 *)
%Y A193979 Cf. A193842, A193980.
%K A193979 nonn,tabl
%O A193979 0,2
%A A193979 _Clark Kimberling_, Aug 10 2011