%I A158858
%S A158858 3,5,1,7,2,27,9,3,54,9,11,4,81,18,243,13,5,108,27,486,81,15,6,135,36,
%T A158858 729,162,2187,17,7,162,45,972,243,4374,729,19,8,189,54,1215,324,6561,
%U A158858 1458,19683,21,9,216,63,1458,405,8748,2187,39366,6561
%N A158858 Triangle T(n,k) =3^(k-1)*e(n,k) read by rows, where e(n,k)= (e(n - 1, 
               k)*e(n, k - 1) + 1)/e(n - 1, k - 1).
%D A158858 H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp 159-162.
%F A158858 Row sums are (5-(-1)^n)*3^n/4-3*n/2.
%F A158858 T(n,k) = 3^(k-1)*e(n,k) where e(n,k)= ( 1+e(n-1,k)*e(n,k-1) )/e(n-1,k-1) 
               and e(n,1)=2*n+1 define a triangle of fractions.
%e A158858 {3},
%e A158858 {5, 1},
%e A158858 {7, 2, 27},
%e A158858 {9, 3, 54, 9},
%e A158858 {11, 4, 81, 18, 243},
%e A158858 {13, 5, 108, 27, 486, 81},
%e A158858 {15, 6, 135, 36, 729, 162, 2187},
%e A158858 {17, 7, 162, 45, 972, 243, 4374, 729},
%e A158858 {19, 8, 189, 54, 1215, 324, 6561, 1458, 19683},
%e A158858 {21, 9, 216, 63, 1458, 405, 8748, 2187, 39366, 6561}
%t A158858 Clear[e, n, k];
%t A158858 e[n_, 0] := 2*n + 1;
%t A158858 e[n_, k_] := 0 /; k >= n;
%t A158858 e[n_, k_] := (e[n - 1, k]*e[n, k - 1] + 1)/e[n - 1, k - 1];
%t A158858 Table[Table[3^k*e[n, k], {k, 0, n - 1}], {n, 1, 10}];
%t A158858 Flatten[%]
%Y A158858 A130303
%Y A158858 Sequence in context: A122053 A124084 A133045 this_sequence A152204 A114216 
               A086233
%Y A158858 Adjacent sequences: A158855 A158856 A158857 this_sequence A158859 A158860 
               A158861
%K A158858 nonn,tabl
%O A158858 1,1
%A A158858 Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Mar 
               28 2009
%E A158858 Edited by the Associate Editors of the OEIS, Apr 22 2009