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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

Table of n, a(n) for n=0..77.

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);

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 October 23 06:29 EDT 2018. Contains 316520 sequences. (Running on oeis4.)