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 A106268 Number triangle T(n,k) = binomial(k-n, n-k)*(-1)^(n-k) = (0^(n-k) + binomial(2*(n-k), n-k))/2 if k <= n, 0 otherwise; Riordan array (1/(2-C(x)), x) where C(x) is g.f. for Catalan numbers A000108. 2
 1, 1, 1, 3, 1, 1, 10, 3, 1, 1, 35, 10, 3, 1, 1, 126, 35, 10, 3, 1, 1, 462, 126, 35, 10, 3, 1, 1, 1716, 462, 126, 35, 10, 3, 1, 1, 6435, 1716, 462, 126, 35, 10, 3, 1, 1, 24310, 6435, 1716, 462, 126, 35, 10, 3, 1, 1, 92378, 24310, 6435, 1716, 462, 126, 35, 10, 3, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Triangle includes A088218. Rows sums are A024718. Diagonal sums are A106269. Inverse is A106270. LINKS EXAMPLE Triangle begins    1;    1,  1;    3,  1,  1;   10,  3,  1,  1;   35, 10,  3,  1,  1; Production matrix begins:     1, 1;     2, 0, 1;     5, 0, 0, 1;    14, 0, 0, 0, 1;    42, 0, 0, 0, 0, 1;   132, 0, 0, 0, 0, 0, 1;   429, 0, 0, 0, 0, 0, 0, 1;   ... - Philippe Deléham, Oct 02 2014 PROG (PARI) trg(nn) = {for (n=1, nn, for (k=1, n, print1(binomial(k-n, n-k)*(-1)^(n-k), ", "); ); print(); ); } \\ Michel Marcus, Oct 03 2014 CROSSREFS Sequence in context: A267392 A267553 A268115 * A267655 A263864 A060543 Adjacent sequences:  A106265 A106266 A106267 * A106269 A106270 A106271 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Apr 28 2005 STATUS approved

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Last modified March 20 05:34 EDT 2019. Contains 321344 sequences. (Running on oeis4.)