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Alternating sums of vertically aligned numbers in Pascal's triangle: T(n,k) = C(n,k) - C(n-2,k-1) + C(n-4,k-2) - ... +- C(n-2[n/2],m).
4

%I #7 May 10 2013 12:44:26

%S 1,1,1,1,1,1,1,2,2,1,1,3,5,3,1,1,4,8,8,4,1,1,5,12,15,12,5,1,1,6,17,27,

%T 27,17,6,1,1,7,23,44,55,44,23,7,1,1,8,30,67,99,99,67,30,8,1,1,9,38,97,

%U 166,197,166,97,38,9,1,1,10,47,135,263,363,363

%N Alternating sums of vertically aligned numbers in Pascal's triangle: T(n,k) = C(n,k) - C(n-2,k-1) + C(n-4,k-2) - ... +- C(n-2[n/2],m).

%F G.f.: 1/(1-(1+y)*x)/(1+y*x^2). - _Vladeta Jovovic_, Oct 12 2003

%e Rows: {1}; {1,1}; {1,1,1}; {1,2,2,1}; {1,3,5,3,1} ...

%Y For (nonalternating) vertically aligned sums, see A013580.

%Y Row sums of this array: A007910.

%K nonn,tabl

%O 0,8

%A _Clark Kimberling_