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A086872 Triangle T(n, k) read by rows; given by [1, 2, 3, 4, 5, 6, ..] DELTA [1, 4, 9, 16, 25, 36, ...] where DELTA is the operator defined in A084938.

%I A086872 #15 Aug 08 2015 10:43:00
%S A086872 1,1,1,3,8,5,15,75,121,61,105,840,2478,3128,1385,945,11025,51030,
%T A086872 115350,124921,50521,10395,166320,1105335,3859680,7365633,7158128,
%U A086872 2702765
%N A086872 Triangle T(n, k) read by rows; given by [1, 2, 3, 4, 5, 6, ..] DELTA [1, 4, 9, 16, 25, 36, ...] where DELTA is the operator defined in A084938.
%H A086872 Alois P. Heinz, <a href="/A086872/b086872.txt">Rows n = 0..140, flattened</a>
%F A086872 Sum( k>=0, T(n, k)*(-1)^k ) = 0; if n>0.
%F A086872 Sum( k>=0, T(n, k)*(-1/2)^k ) = (1/2)^n.
%F A086872 Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = (-1)^n*A121822(n), (-1)^n*A092812(n), (-1)^n*A054879(n), A009117(n), A033999(n), A000007(n), A000364(n), A000182(n+1) for x = -6, -5, -4, -3, -2, -1, 0, 1 respectively .
%e A086872 Triangle begins:
%e A086872 1;
%e A086872 1, 1;
%e A086872 3, 8, 5;
%e A086872 15, 75, 121, 61;
%e A086872 105, 840, 2478, 3128, 1385;
%e A086872 945, 11025, 51030, 115350, 124921, 50521;
%e A086872 10395, 166320, 1105335, 3859680, 7365633, 7158128, 2702765 ; ...
%Y A086872 Cf. A000182 (row sums), A000364 (first diagonal), A001147 (first column), A084938, A261065 (2nd column).
%K A086872 easy,nonn,tabl
%O A086872 0,4
%A A086872 _Philippe Deléham_, Aug 20 2003, Aug 17 2007