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