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 A205813 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. 4
 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, 0, 924, 1024, 630, 256, 70, 12, 1, 0, 3432, 4096, 2772, 1280, 420, 96, 14, 1, 0, 12870, 16384, 12012, 6144, 2310, 640, 126, 16, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Riordan array (1, x/sqrt(1-4x)). Inverse of Riordan array (1, x*exp(arcsinh(-2x)). LINKS FORMULA T(n,n) = 1 = A000012(n); T(n+1,n) = 2n = A005843(n); T(n+2,n) = 2n*(n+2) = A054000(n+1). 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. G.f.: sqrt(1-4x)/(sqrt(1-4x)-y*x). Sum_{k=0..n} T(n,k)*A090192(k) = A000108(n), A000108 = Catalan numbers. EXAMPLE Triangle begins:   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; CROSSREFS Cf. A054335 and columns listed there. Sequence in context: A011312 A275328 A147720 * A127631 A122538 A090238 Adjacent sequences:  A205810 A205811 A205812 * A205814 A205815 A205816 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Feb 01 2012 STATUS approved

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Last modified June 5 16:19 EDT 2020. Contains 334852 sequences. (Running on oeis4.)