cp's OEIS Frontend

A193850 Triangular array: the fission of ((x+2)^n) by (q(n,x)) given by q(n,x)=x^n+x^(n-1)+...+x+1.

%I A193850 #6 Mar 30 2012 18:57:38
%S A193850 2,4,8,8,20,26,16,48,72,80,32,112,192,232,242,64,256,496,656,716,728,
%T A193850 128,576,1248,1808,2088,2172,2186,256,1280,3072,4864,5984,6432,6544,
%U A193850 6560,512,2816,7424,12800,16832,18848,19520,19664,19682,1024,6144
%N A193850 Triangular array:  the fission of ((x+2)^n) by (q(n,x)) given by q(n,x)=x^n+x^(n-1)+...+x+1.
%C A193850 See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.
%e A193850 First six rows:
%e A193850 2
%e A193850 4....8
%e A193850 8....20....26
%e A193850 16...48....72....80
%e A193850 32...112...192...232....242
%e A193850 64...256...496...656....716...728
%t A193850 z = 10;
%t A193850 p[n_, x_] := (x + 2)^n;
%t A193850 q[0, x_] := 1; q[n_, x_] := x*q[n - 1, x] + 1;
%t A193850 p1[n_, k_] := Coefficient[p[n, x], x^k];
%t A193850 p1[n_, 0] := p[n, x] /. x -> 0;
%t A193850 d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
%t A193850 h[n_] := CoefficientList[d[n, x], {x}]
%t A193850 TableForm[Table[Reverse[h[n]], {n, 0, z}]]
%t A193850 Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193850 *)
%t A193850 TableForm[Table[h[n], {n, 0, z}]]
%t A193850 Flatten[Table[h[n], {n, -1, z}]]   (* A193851  *)
%t A193850 TableForm[Table[Reverse[h[n]/2], {n, 0, z}]]
%t A193850 Flatten[Table[Reverse[h[n]]/2, {n, -1, z}]] (* A193852 *)
%t A193850 TableForm[Table[h[n]/2, {n, 0, z}]]
%t A193850 Flatten[Table[h[n]/2, {n, -1, z}]]  (* A193853 *)
%Y A193850 Cf. A193842, A193850, A193852.
%K A193850 nonn,tabl
%O A193850 0,1
%A A193850 _Clark Kimberling_, Aug 07 2011