

A165408


An aerated Catalan array.


3



1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 2, 0, 4, 0, 1, 0, 0, 0, 5, 0, 5, 0, 1, 0, 0, 0, 0, 9, 0, 6, 0, 1, 0, 0, 0, 5, 0, 14, 0, 7, 0, 1, 0, 0, 0, 0, 14, 0, 20, 0, 8, 0, 1, 0, 0, 0, 0, 0, 28, 0, 27, 0, 9, 0, 1, 0, 0, 0, 0, 14, 0, 48, 0, 35, 0, 10, 0, 1, 0, 0, 0, 0, 0, 42, 0, 75, 0
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OFFSET

0,13


COMMENTS

Aeration of A120730. Row sums are A165407.


LINKS

Table of n, a(n) for n=0..99.


FORMULA

Number triangle T(n,k)=if(n<=3k, C((n+k)/2,k)*((3kn)/2+1)*(1+(1)^(nk))/(2(k+1)),0);
G.f.: 1/(1xyx^3y/(1x^3y/(1x^3y/(1x^3y/(1... (continued fraction).


EXAMPLE

Triangle begins
1,
0, 1,
0, 0, 1,
0, 1, 0, 1,
0, 0, 2, 0, 1,
0, 0, 0, 3, 0, 1,
0, 0, 2, 0, 4, 0, 1,
0, 0, 0, 5, 0, 5, 0, 1,
0, 0, 0, 0, 9, 0, 6, 0, 1,
0, 0, 0, 5, 0, 14, 0, 7, 0, 1,
0, 0, 0, 0, 14, 0, 20, 0, 8, 0, 1,
0, 0, 0, 0, 0, 28, 0, 27, 0, 9, 0, 1,
0, 0, 0, 0, 14, 0, 48, 0, 35, 0, 10, 0, 1


CROSSREFS

Sequence in context: A187144 A123635 A124304 * A186733 A171368 A322353
Adjacent sequences: A165405 A165406 A165407 * A165409 A165410 A165411


KEYWORD

easy,nonn,tabl


AUTHOR

Paul Barry, Sep 17 2009


STATUS

approved



