%I A123097
%S A123097 1,3,2,4,7,3,5,14,13,4,6,23,33,21,5,7,34,66,64,31,6,8,47,115,150,110,43,
%T A123097 7,9,62,183,300,295,174,57,8,10,79,273,539,665,525,259,73,9,11,98,388,
%U A123097 896,1330,1316,868,368,91,10,12,119,531,1404,2436,2898,2394,1356,504
%N A123097 Triangle read by rows: T(n,k)=binom(n-2,k-1)+n*binom(n-1,k-1), 1<=k<=n.
%C A123097 Triangle is M*P, where M is the infinite bidiagonal matrix with (1,2,
               3...) in the main diagonal and (1,1,1...) in the subdiagonal and 
               P is Pascal's triangle as an infinite lower triangular matrix. The 
               triangle A124727=P*M.
%e A123097 First few rows of the triangle are:
%e A123097 1;
%e A123097 3, 2;
%e A123097 4, 7, 3;
%e A123097 5, 14, 13, 4
%e A123097 6, 23, 33, 21, 5;
%e A123097 7, 34, 66, 64, 31, 6;
%e A123097 ...
%p A123097 T:=proc(n,k) if n=1 and k=1 then 1 elif n=1 then 0 else binomial(n-2,
               k-1)+n*binomial(n-1,k-1) fi end: for n from 1 to 12 do seq(T(n,k),
               k=1..n) od; # yields sequence in triangular form
%Y A123097 Row sums = A052951: (1, 5, 14, 36, 88, 208...)
%Y A123097 Sequence in context: A085346 A121861 A060006 this_sequence A134571 A054086 
               A163329
%Y A123097 Adjacent sequences: A123094 A123095 A123096 this_sequence A123098 A123099 
               A123100
%K A123097 nonn,tabl
%O A123097 1,2
%A A123097 Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Nov 05 2006
%E A123097 Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 24 2006