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A172381 Triangle whose inverse has production matrix with general term (-1)^(n-k+1)*C(k+1, n-k+1).

%I A172381 #2 Mar 30 2012 18:59:26
%S A172381 1,1,1,2,3,1,5,10,6,1,14,36,31,10,1,42,137,156,75,15,1,132,544,787,
%T A172381 510,155,21,1,429,2235,4017,3331,1380,287,28,1,1430,9445,20809,21405,
%U A172381 11411,3255,490,36,1,4862,40876,109486,136921,90665,33390,6916,786,45,1,16796
%N A172381 Triangle whose inverse has production matrix with general term (-1)^(n-k+1)*C(k+1, n-k+1).
%C A172381 Product of A033184 and A172380. Diagonal sums are A172382(n+2).
%e A172381 Triangle begins
%e A172381 1,
%e A172381 1, 1,
%e A172381 2, 3, 1,
%e A172381 5, 10, 6, 1,
%e A172381 14, 36, 31, 10, 1,
%e A172381 42, 137, 156, 75, 15, 1,
%e A172381 132, 544, 787, 510, 155, 21, 1,
%e A172381 429, 2235, 4017, 3331, 1380, 287, 28, 1,
%e A172381 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1,
%e A172381 4862, 40876, 109486, 136921, 90665, 33390, 6916, 786, 45, 1,
%e A172381 16796, 180544, 584955, 877252, 704720, 322728, 86443, 13536, 1200, 55, 1
%e A172381 Production array of inverse is
%e A172381 -1, 1,
%e A172381 0, -2, 1,
%e A172381 0, 1, -3, 1,
%e A172381 0, 0, 3, -4, 1,
%e A172381 0, 0, -1, 6, -5, 1,
%e A172381 0, 0, 0, -4, 10, -6, 1,
%e A172381 0, 0, 0, 1, -10, 15, -7, 1,
%e A172381 0, 0, 0, 0, 5, -20, 21, -8, 1,
%e A172381 0, 0, 0, 0, -1, 15, -35, 28, -9, 1,
%e A172381 0, 0, 0, 0, 0, -6, 35, -56, 36, -10, 1,
%e A172381 0, 0, 0, 0, 0, 1, -21, 70, -84, 45, -11, 1
%K A172381 nonn,tabl
%O A172381 0,4
%A A172381 _Paul Barry_, Feb 01 2010