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A106187 Sequence array for central binomial numbers A000984.

%I A106187 #16 Apr 22 2025 06:31:53
%S A106187 1,2,1,6,2,1,20,6,2,1,70,20,6,2,1,252,70,20,6,2,1,924,252,70,20,6,2,1,
%T A106187 3432,924,252,70,20,6,2,1,12870,3432,924,252,70,20,6,2,1,48620,12870,
%U A106187 3432,924,252,70,20,6,2,1,184756,48620,12870,3432,924,252,70,20,6,2,1
%N A106187 Sequence array for central binomial numbers A000984.
%F A106187 T(n, k) = binomial(2*(n-k), n-k).
%F A106187 Riordan array (1/sqrt(1-4x), x).
%e A106187 Triangle begins:
%e A106187     1;
%e A106187     2,  1;
%e A106187     6,  2, 1;
%e A106187    20,  6, 2, 1;
%e A106187    70, 20, 6, 2, 1;
%e A106187   252, 70, 20, 6, 2, 1;
%e A106187   ...
%e A106187 The matrix inverse starts:
%e A106187    1;
%e A106187   -2,1;
%e A106187   -2,-2,1;
%e A106187   -4,-2,-2,1;
%e A106187   -10,-4,-2,-2,1;
%e A106187   -28,-10,-4,-2,-2,1;
%e A106187   -84,-28,-10,-4,-2,-2,1;
%e A106187   -264,-84,-28,-10,-4,-2,-2,1;
%e A106187 apparently related to A002420. - _R. J. Mathar_, Apr 08 2013
%p A106187 A106187 := proc(n,k)
%p A106187     binomial(2*(n-k),n-k) ;
%p A106187 end proc: # _R. J. Mathar_, Apr 08 2013
%t A106187 T[n_, k_] := (((2*n - 2*k)!)/((n - k)!)^2); Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Detlef Meya_, Aug 11 2024 *)
%Y A106187 Row sums are A006134.
%Y A106187 Antidiagonal sums are A106188.
%Y A106187 Cf. A000984.
%K A106187 easy,nonn,tabl
%O A106187 0,2
%A A106187 _Paul Barry_, Apr 24 2005