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A096801 Triangle, read by rows, that transforms the (n+m)-dimensional partitions of n into the (n+m+1)-dimensional partitions of n, for fixed m.

%I A096801 #3 Mar 30 2012 18:36:41
%S A096801 1,0,1,0,1,1,0,2,1,1,0,7,3,1,1,0,26,10,4,1,1,0,124,44,13,5,1,1,0,640,
%T A096801 218,68,16,6,1,1,0,3695,1208,332,99,19,7,1,1,0,23231,7403,2100,457,
%U A096801 138,22,8,1,1,0,156572,48663,12566,3518,579,186,25,9,1,1,0,1133838,346636
%N A096801 Triangle, read by rows, that transforms the (n+m)-dimensional partitions of n into the (n+m+1)-dimensional partitions of n, for fixed m.
%C A096801 Transforms any diagonal of A096751 (square table of n-dimensional partitions) into the next lower diagonal in the table. It is not yet certain if this triangle contains negative terms.
%e A096801 The main diagonal of A096751: {1,1,3,10,45,216,...} (A096752),
%e A096801 is transformed into the secondary diagonal: {1,1,4,15,71,357,...},
%e A096801 as demonstrated by the dot product of row #5 with A096752:
%e A096801 [0,26,10,4,1,1]*[1,1,3,10,45,216] = 357.
%e A096801 Rows begin:
%e A096801 [1],
%e A096801 [0,1],
%e A096801 [0,1,1],
%e A096801 [0,2,1,1],
%e A096801 [0,7,3,1,1],
%e A096801 [0,26,10,4,1,1],
%e A096801 [0,124,44,13,5,1,1],
%e A096801 [0,640,218,68,16,6,1,1],
%e A096801 [0,3695,1208,332,99,19,7,1,1],
%e A096801 [0,23231,7403,2100,457,138,22,8,1,1],
%e A096801 [0,156572,48663,12566,3518,579,186,25,9,1,1],
%e A096801 [0,1133838,346636,94878,18043,5787,679,244,28,10,1,1],
%e A096801 [0,8635777,2590866,623351,188962,20539,9391,733,313,31,11,1,1],
%e A096801 [0,70212042,20875236,5828851,762072,398052,13238,15009,712,394,34,12,1,1],...
%Y A096801 Cf. A096751, A096752, A096802 (row sums), A096803-A096805 (columns).
%K A096801 nonn,tabl
%O A096801 0,8
%A A096801 _Paul D. Hanna_, Jul 13 2004