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%I #8 Feb 22 2013 14:39:46
%S 1,1,1,3,6,3,5,17,19,7,11,48,80,60,17,21,119,270,308,177,41,43,290,
%T 823,1256,1087,506,99,85,677,2321,4447,5147,3601,1411,239,171,1556,
%U 6234,14360,20806,19424,11416,3864,577
%N Triangle T(n,k), read by rows, given by (1, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 2, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C Antidiagonal sums are in A077995.
%F G.f.: (1-y*x)/(1-(1+2*y)*x-(2+3*y+y^2)*x^2)
%F T(n,k) = T(n-1,k) + 2*T(n-1,k-1) + 2*T(n-2,k) + 3*T(n-2,k-1) + T(n-2,k-2), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = T(2,2) = 3, T(2,1) = 6 and T(n,k) = 0 if k<0 or if k>n.
%F T(n,n) = A001333(n), T(n,0) = A001045(n+1).
%F Sum_{k, 0<=k<=n} T(n,k)*(-1)^k = A000007(n).
%e Triangle begins
%e 1
%e 1, 1
%e 3, 6, 3
%e 5, 17, 19, 7
%e 11, 48, 80, 60, 17
%e 21, 119, 270, 308, 177, 41
%e 43, 290, 823, 1256, 1087, 506, 99
%e 85, 677, 2321, 4447, 5147, 3601, 1411, 239
%Y Cf. A001045, A001333, A077995,
%K easy,nonn,tabl
%O 0,4
%A _Philippe Deléham_, Apr 27 2012