cp's OEIS Frontend

A119865 Triangle T(n,k), 0<=k<=n, read by rows, given by [1, 1, 0, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.

%I A119865 #11 Nov 09 2013 10:14:30
%S A119865 1,1,1,2,3,1,4,9,6,1,8,25,26,10,1,16,65,95,60,15,1,32,161,308,279,120,
%T A119865 21,1,64,385,917,1099,693,217,28,1,128,897,2566,3856,3256,1526,364,36,
%U A119865 1
%N A119865 Triangle T(n,k), 0<=k<=n, read by rows, given by [1, 1, 0, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
%F A119865 Sum_{k =0..n}T(n,k)= A087944(n).
%F A119865 Sum_{k=0..n}(-1)^k*2^(n-k)*T(n,k)= n^2-n+1= A002061(n).
%F A119865 Sum_{k=0..n}(-1)^k*T(n,k)=0^n= A000007(n).
%F A119865 G.f.: (1-2*x-2*x*y++x^2+x^2*y+x^2*y^2)/(1-3*x-3*x*y+2*x^2+4*x^2*y+3*x^2*y^2-x^3*y^2-x^3*y^3). - _Philippe Deléham_, Nov 09 2013
%F A119865 T(n,k) = 3*T(n-1,k) + 3*T(n-1,k-1) - 2*T(n-2,k) - 4*T(n-2,k-1) - 3*T(n-2,k-2) + T(n-3,k-2) + T(n-3,k-3), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 3, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Nov 09 2013
%e A119865 Triangle begins:
%e A119865 1;
%e A119865 1, 1;
%e A119865 2, 3, 1;
%e A119865 4, 9, 6, 1;
%e A119865 8, 25, 26, 10, 1;
%e A119865 16, 65, 95, 60, 15, 1;
%e A119865 32, 161, 308, 279, 120, 21, 1;
%e A119865 64, 385, 917, 1099, 693, 217, 28, 1;
%e A119865 128, 897, 2566, 3856, 3256, 1526, 364, 36, 1;
%Y A119865 Cf. Diagonals : A011782, A002064 ; A000012, A000217.
%K A119865 easy,nonn,tabl
%O A119865 0,4
%A A119865 _Philippe Deléham_, Jul 31 2006