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A189230 Complementary Catalan triangle read by rows.

%I A189230 #12 May 08 2020 17:45:33
%S A189230 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,
%T A189230 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,
%U A189230 480,0,270,0,80,0,10,0,462,0,990,0,825,0,385,0,99,0,11,0
%N A189230 Complementary Catalan triangle read by rows.
%C A189230 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).
%C A189230 T(n,0) = A138364(n). Row sums: A100071.
%H A189230 Peter Luschny, <a href="/A180000/a180000.pdf">Die schwingende Fakultät und Orbitalsysteme</a>, August 2011.
%H A189230 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/TheLostCatalanNumbers">The lost Catalan numbers</a>
%e A189230 [0]  0,
%e A189230 [1]  1,  0,
%e A189230 [2]  0,  2,  0,
%e A189230 [3]  3,  0,  3,  0,
%e A189230 [4]  0,  8,  0,  4,  0,
%e A189230 [5] 10,  0, 15,  0,  5, 0,
%e A189230 [6]  0, 30,  0, 24,  0, 6, 0,
%e A189230 [7] 35,  0, 63,  0, 35, 0, 7, 0,
%e A189230    [0],[1],[2],[3],[4],[5],[6],[7]
%p A189230 A189230 := (n,k) -> A189231(n,k)*modp(n-k,2):
%p A189230 seq(print(seq(A189230(n,k),k=0..n)),n=0..11);
%t A189230 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 A189230 T[n_, k_] := t[n, k] Mod[n-k, 2];
%t A189230 Table[T[n, k], {n, 0, 11}, {k, 0, n}] (* _Jean-François Alcover_, Jun 24 2019 *)
%Y A189230 Cf. A053121, A162246, A057977, A189231.
%K A189230 nonn,tabl
%O A189230 0,5
%A A189230 Peter Luschny, May 01 2011