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A159924 Triangle read by rows: a(m,m) = 1, for all m. For n < m, a(m,n) = a(m-1,n) + (sum of all terms in rows 1 through m-1).

%I A159924 #16 Sep 24 2017 02:32:03
%S A159924 1,2,1,6,5,1,22,21,17,1,99,98,94,78,1,546,545,541,525,448,1,3599,3598,
%T A159924 3594,3578,3501,3054,1,27577,27576,27572,27556,27479,27032,23979,1,
%U A159924 240327,240326,240322,240306,240229,239782,236729,212751,1,2343850
%N A159924 Triangle read by rows: a(m,m) = 1, for all m. For n < m, a(m,n) = a(m-1,n) + (sum of all terms in rows 1 through m-1).
%C A159924 Row sums are A159925. Sum of all terms in rows 1 through m is A159926(m). A159926(m) - A159926(m-1) = A159925(m), for m >= 2.
%H A159924 Michael De Vlieger, <a href="/A159924/b159924.txt">Table of n, a(n) for n = 1..11476</a> (rows 1 <= n <= 150).
%e A159924 The triangle starts like this:
%e A159924 1,
%e A159924 2,1,
%e A159924 6,5,1,
%e A159924 22,21,17,1
%e A159924 The sum of all these terms is 77. So adding 77 to each of the terms of the 4th row gets the fifth row: 22+77=99, 21+77=98, 17+77=94, 1+77=78, and the final terms is set at 1. So row 5 is: 99,98,94,78,1.
%p A159924 A159924 := proc(n,m) option remember ; local s; if n = m then 1; else s := add(add(procname(r,c),c=1..r),r=1..n-1) ; procname(n-1,m)+s ; fi; end: for n from 1 to 13 do for m from 1 to n do printf("%d,",A159924(n,m)) ; od: od: # _R. J. Mathar_, Apr 29 2009
%t A159924 Block[{m = 0}, NestList[Block[{w = #}, AddTo[m, Total@ w]; Append[m + w, 1]] &, {1}, 9]] // Flatten (* _Michael De Vlieger_, Sep 23 2017 *)
%Y A159924 Cf. A159925, A159926, A159927.
%K A159924 nonn,tabl
%O A159924 1,2
%A A159924 _Leroy Quet_, Apr 26 2009
%E A159924 More terms from _R. J. Mathar_, Apr 29 2009