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A159930 Triangle read by rows: a(1,1)=1. a(m,n) = a(m-1,n) + (sum of all terms in row m-1), for n a(m,m) = sum of all terms in row m-1.

%I A159930 #19 Sep 07 2024 15:40:25
%S A159930 1,2,1,5,4,3,17,16,15,12,77,76,75,72,60,437,436,435,432,420,360,2957,
%T A159930 2956,2955,2952,2940,2880,2520,23117,23116,23115,23112,23100,23040,
%U A159930 22680,20160,204557,204556,204555,204552,204540,204480,204120,201600
%N A159930 Triangle read by rows: a(1,1)=1. a(m,n) = a(m-1,n) + (sum of all terms in row m-1), for n<m. a(m,m) = sum of all terms in row m-1.
%C A159930 The sum of all terms in row m is (m+1)!/2. So a(m,n) = a(m-1,n) + m!/2, or is m!/2 if n=m.
%C A159930 Sum of m-th row = A001710(m+1). [_Klaus Brockhaus_, Jun 02 2009]
%C A159930 First column is A014288. - _Franklin T. Adams-Watters_, Oct 19 2013
%e A159930 Triangle starts:
%e A159930 1;
%e A159930 2, 1;
%e A159930 5, 4, 3;
%e A159930 17, 16, 15, 12;
%e A159930 77, 76, 75, 72, 60;
%o A159930 (Magma) S:=[1]; T:=S; for m in [2..9] do s:=&+T; T:=[ n lt m select T[n]+s else s: n in [1..m] ]; S:=S cat T; end for; S; // _Klaus Brockhaus_, Jun 02 2009
%Y A159930 Cf. A159927.
%K A159930 nonn,tabl
%O A159930 1,2
%A A159930 _Leroy Quet_, Apr 26 2009
%E A159930 More terms from _Klaus Brockhaus_, Jun 02 2009