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 A189230 Complementary Catalan triangle read by rows. 3
 0, 1, 0, 0, 2, 0, 3, 0, 3, 0, 0, 8, 0, 4, 0, 10, 0, 15, 0, 5, 0, 0, 30, 0, 24, 0, 6, 0, 35, 0, 63, 0, 35, 0, 7, 0, 0, 112, 0, 112, 0, 48, 0, 8, 0, 126, 0, 252, 0, 180, 0, 63, 0, 9, 0, 0, 420, 0, 480, 0, 270, 0, 80, 0, 10, 0, 462, 0, 990, 0, 825, 0, 385, 0, 99, 0, 11, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n,k) = A189231(n,k)*((n - k) mod 2). For comparison: the classical Catalan triangle is A053121(n,k) = A189231(n,k)*((n-k+1) mod 2). T(n,0) = A138364(n). Row sums: A100071. REFERENCES Peter Luschny, Divide, swing and conquer the factorial and the lcm{1,2,...,n}, preprint, April 2008. LINKS Peter Luschny, The lost Catalan numbers EXAMPLE [0]  0, [1]  1,  0, [2]  0,  2,  0, [3]  3,  0,  3,  0, [4]  0,  8,  0,  4,  0, [5] 10,  0, 15,  0,  5, 0, [6]  0, 30,  0, 24,  0, 6, 0, [7] 35,  0, 63,  0, 35, 0, 7, 0,    [0],[1],[2],[3],[4],[5],[6],[7] MAPLE A189230 := (n, k) -> A189231(n, k)*modp(n-k, 2): seq(print(seq(A189230(n, k), k=0..n)), n=0..11); MATHEMATICA t[n_, k_] /; (k>n || k<0) = 0; t[n_, n_] = 1; t[n_, k_] := t[n, k] = t[n-1, k-1] + Mod[n-k, 2] t[n-1, k] + t[n-1, k+1]; T[n_, k_] := t[n, k] Mod[n-k, 2]; Table[T[n, k], {n, 0, 11}, {k, 0, n}] (* Jean-François Alcover, Jun 24 2019 *) CROSSREFS Cf. A053121, A162246, A057977, A189231. Sequence in context: A011374 A298645 A243319 * A243982 A214000 A161123 Adjacent sequences:  A189227 A189228 A189229 * A189231 A189232 A189233 KEYWORD nonn,tabl AUTHOR Peter Luschny, May 01 2011 STATUS approved

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Last modified July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)