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%I A177978 #9 Dec 17 2019 05:34:14
%S A177978 1,0,1,0,-1,1,0,1,-1,1,0,-1,0,-1,1,0,1,1,0,-1,1,0,-1,-1,0,0,-1,1,0,1,
%T A177978 0,1,0,0,-1,1,0,-1,1,-1,0,0,0,-1,1,0,1,-1,0,1,0,0,0,-1,1,0,-1,0,0,-1,
%U A177978 0,0,0,0,-1,1,0,1,1,1,0,1,0,0,0,0,-1,1,0,-1,-1,-1,0,-1,0,0,0,0,0,-1,1,0,1
%N A177978 Triangle T(n,k) read by rows: A051731(n,k) - A051731(n-1,k).
%C A177978 The recurrence for this triangle is similar to the recurrence in A177517. Cumulative column sums give table A051731.
%F A177978 T(n,1)=A000007, k > 1: T(n,k) = (Sum_{i=1..k-1} T(n-i,k-1)) - (Sum_{i=1..k-1} T(n-i,k)).
%e A177978 Triangle begins:
%e A177978   1;
%e A177978   0,  1;
%e A177978   0, -1,  1;
%e A177978   0,  1, -1,  1;
%e A177978   0, -1,  0, -1,  1;
%e A177978   0,  1,  1,  0, -1,  1;
%e A177978   0, -1, -1,  0,  0, -1,  1;
%e A177978   0,  1,  0,  1,  0,  0, -1,  1;
%e A177978   0, -1,  1, -1,  0,  0,  0, -1,  1;
%e A177978   0,  1, -1,  0,  1,  0,  0,  0, -1,  1;
%e A177978   0, -1,  0,  0, -1,  0,  0,  0,  0, -1,  1;
%e A177978   0,  1,  1,  1,  0,  1,  0,  0,  0,  0, -1,  1;
%e A177978   0, -1, -1, -1,  0, -1,  0,  0,  0,  0,  0, -1,  1;
%e A177978   0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0, -1,  1;
%o A177978 (Excel cell formula, American) =if(column()=1, if(row()>1,0,1), if(row()>=column(), sum(indirect(address(row()-column()+1, column()-1, 4)&":"&address(row()-1, column()-1, 4), 4))-sum(indirect(address(row()-column()+1, column(), 4)&":"&address(row()-1, column(), 4), 4)), 0))
%o A177978 (Excel cell formula, European)=if(column()=1; if(row()>1;0;1); if(row()>=column(); sum(indirect(address(row()-column()+1; column()-1; 4)&":"&address(row()-1; column()-1; 4); 4))-sum(indirect(address(row()-column()+1; column(); 4)&":"&address(row()-1; column(); 4); 4)); 0))
%Y A177978 Matrix inverse of A134540. Cf. A177517.
%K A177978 sign,tabl
%O A177978 1,1
%A A177978 _Mats Granvik_, May 16 2010
%E A177978 Typo in sequence (erroneous comma) corrected by _N. J. A. Sloane_, May 22 2010
%E A177978 Edited by _Mats Granvik_, Dec 11 2010

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