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A158860 Triangle T(n,k)= ( 1 +T(n-1,k)*T(n,k-1) ) / T(n-1,k-1) initialized by T(n,0)=3n-2, T(n,k)=0 if k>=n, read by rows 0<=k

%I A158860 #5 Jul 11 2012 11:24:36
%S A158860 1,4,1,7,2,1,10,3,2,1,13,4,3,2,1,16,5,4,3,2,1,19,6,5,4,3,2,1,22,7,6,5,
%T A158860 4,3,2,1,25,8,7,6,5,4,3,2,1,28,9,8,7,6,5,4,3,2,1
%N A158860 Triangle T(n,k)= ( 1 +T(n-1,k)*T(n,k-1) ) / T(n-1,k-1) initialized by T(n,0)=3n-2, T(n,k)=0 if k>=n, read by rows 0<=k<n.
%C A158860 Row sums are in A052905.
%D A158860 H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp 159-162.
%F A158860 T(n,k) = n-k, k>=1. - _R. J. Mathar_, Jul 11 2012
%e A158860 1;
%e A158860 4, 1;
%e A158860 7, 2, 1;
%e A158860 10, 3, 2, 1;
%e A158860 13, 4, 3, 2, 1;
%e A158860 16, 5, 4, 3, 2, 1;
%e A158860 19, 6, 5, 4, 3, 2, 1;
%e A158860 22, 7, 6, 5, 4, 3, 2, 1;
%e A158860 25, 8, 7, 6, 5, 4, 3, 2, 1;
%e A158860 28, 9, 8, 7, 6, 5, 4, 3, 2, 1;
%p A158860 A158860 := proc(n,k)
%p A158860     option remember;
%p A158860     if k = 0 then
%p A158860         3*n-2 ;
%p A158860     elif k >= n then
%p A158860         0 ;
%p A158860     else
%p A158860         (1+procname(n-1,k)*procname(n,k-1))/procname(n-1,k-1) ;
%p A158860     end if;
%p A158860 end proc: # _R. J. Mathar_, Jul 11 2012
%t A158860 Clear[e, n, k];
%t A158860 e[n_, 0] := 3*n - 2;
%t A158860 e[n_, k_] := 0 /; k >= n;
%t A158860 e[n_, k_] := (e[n - 1, k]*e[n, k - 1] + 1)/e[n - 1, k - 1];
%t A158860 Table[Table[e[n, k], {k, 0, n - 1}], {n, 1, 10}];
%t A158860 Flatten[%]
%Y A158860 Cf. A130303
%K A158860 nonn,easy,tabl
%O A158860 1,2
%A A158860 _Roger L. Bagula_ and _Gary W. Adamson_, Mar 28 2009