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%I #18 Oct 19 2022 11:27:00
%S 1,0,1,0,2,1,0,6,4,1,0,20,16,6,1,0,70,64,30,8,1,0,252,256,140,48,10,1,
%T 0,924,1024,630,256,70,12,1,0,3432,4096,2772,1280,420,96,14,1,0,12870,
%U 16384,12012,6144,2310,640,126,16,1
%N Triangle T(n,k), read by rows, given by (0, 2, 1, 1, 1, 1, 1, 1, 1, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C Riordan array (1, x/sqrt(1-4x)). Inverse of Riordan array (1, x*exp(arcsinh(-2x)).
%C T is the convolution triangle of the shifted central binomial coefficients binomial(2*(n-1), n-1). - _Peter Luschny_, Oct 19 2022
%F T(n,n) = 1 = A000012(n); T(n+1,n) = 2n = A005843(n); T(n+2,n) = 2n*(n+2) = A054000(n+1).
%F Sum_{k=0..n} T(n,k)*x^k = -A081696(n-1), A000007(n), A026671(n-1), A084868(n) for x = -1, 0, 1, 2 respectively.
%F G.f.: sqrt(1-4x)/(sqrt(1-4x)-y*x).
%F Sum_{k=0..n} T(n,k)*A090192(k) = A000108(n), A000108 = Catalan numbers.
%e Triangle begins:
%e 1;
%e 0, 1;
%e 0, 2, 1;
%e 0, 6, 4, 1;
%e 0, 20, 16, 6, 1;
%e 0, 70, 64, 30, 8, 1;
%e 0, 252, 256, 140, 48, 10, 1;
%p # Uses function PMatrix from A357368.
%p PMatrix(10, n -> binomial(2*(n-1), n-1)); # _Peter Luschny_, Oct 19 2022
%Y Cf. A054335 and columns listed there.
%K easy,nonn,tabl
%O 0,5
%A _Philippe Deléham_, Feb 01 2012
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