cp's OEIS Frontend

A193977 Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=sum{(k+1)*x^k ; 0<=k<=n}.

%I A193977 #8 Jan 17 2014 10:13:02
%S A193977 2,6,5,12,14,9,20,27,24,14,30,44,45,36,20,42,65,72,66,50,27,56,90,105,
%T A193977 104,90,66,35,72,119,144,150,140,117,84,44,90,152,189,204,200,180,147,
%U A193977 104,54,110,189,240,266,270,255,224,180,126,65,132,230,297,336
%N A193977 Triangular array:  the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=sum{(k+1)*x^k ; 0<=k<=n}.
%C A193977 See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.
%e A193977 First six rows:
%e A193977 2
%e A193977 6....5
%e A193977 12...14...9
%e A193977 20...27...24...14
%e A193977 30...44...45...36...20
%e A193977 42...65...72...66...50...27
%t A193977 z = 11;
%t A193977 p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
%t A193977 q[n_, x_] := Sum[(k + 1)*x^k, {k, 0, n}]
%t A193977 p1[n_, k_] := Coefficient[p[n, x], x^k];
%t A193977 p1[n_, 0] := p[n, x] /. x -> 0;
%t A193977 d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
%t A193977 h[n_] := CoefficientList[d[n, x], {x}]
%t A193977 TableForm[Table[Reverse[h[n]], {n, 0, z}]]
%t A193977 Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193977 *)
%t A193977 TableForm[Table[h[n], {n, 0, z}]]
%t A193977 Flatten[Table[h[n], {n, -1, z}]]  (* A193978 *)
%Y A193977 Cf. A193842, A193978.
%K A193977 nonn,tabl
%O A193977 0,1
%A A193977 _Clark Kimberling_, Aug 10 2011