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Triangle read by rows: T(n,k) = binomial(2(n-k),n-k)/(1-2(n-k)).
2

%I #5 Jul 30 2015 22:48:09

%S 1,-2,1,-2,-2,1,-4,-2,-2,1,-10,-4,-2,-2,1,-28,-10,-4,-2,-2,1,-84,-28,

%T -10,-4,-2,-2,1,-264,-84,-28,-10,-4,-2,-2,1,-858,-264,-84,-28,-10,-4,

%U -2,-2,1,-2860,-858,-264,-84,-28,-10,-4,-2,-2,1,-9724,-2860,-858,-264,-84,-28,-10,-4,-2,-2,1,-33592,-9724,-2860,-858

%N Triangle read by rows: T(n,k) = binomial(2(n-k),n-k)/(1-2(n-k)).

%C Sequence array for expansion of sqrt(1-4x).

%C Row sums are A106191. Diagonal sums are A106192. Sequence array for A002420. Inverse of number triangle A106187.

%C Riordan array (sqrt(1-4x),x).

%e Triangle begins

%e 1;

%e -2,1;

%e -2,-2,1;

%e -4,-2,-2,1;

%e -10,-4,-2,-2,1;

%e -28,-10,-4,-2,-2,1;

%t T[n_, k_] := Binomial[2(n - k), n - k]/(1 - 2(n - k)); Flatten[ Table[ T[n, k], {n, 0, 10}, {k, 0, n}]] (* _Robert G. Wilson v_, Apr 25 2005 *)

%K easy,sign,tabl

%O 0,2

%A _Paul Barry_, Apr 24 2005

%E More terms from _Robert G. Wilson v_, Apr 25 2005