

A178616


Triangle by columns, odd columns of Pascal's triangle A007318, else (1, 0, 0, 0,...)


4



1, 0, 1, 0, 2, 1, 0, 3, 0, 1, 0, 4, 0, 4, 1, 0, 5, 0, 10, 0, 1, 0, 6, 0, 20, 0, 6, 1, 0, 7, 0, 35, 0, 21, 0, 1, 0, 8, 0, 56, 0, 56, 0, 8, 0, 1, 0, 9, 0, 84, 0, 126, 0, 36, 0, 1, 0, 10, 0, 120, 0, 252, 0, 120, 0, 10, 1
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OFFSET

0,5


COMMENTS

Row sums = a variant of A052950, starting (1, 1, 3, 4, 9, 16, 33,...); whereas
A052950 starts (2, 1, 3, 4, 9,...).
Column 1 of the inverse of A178616 is a signed variant of A065619 prefaced
with an 0; where A065619 = (1, 2, 3, 8, 25, 96, 427,...).


LINKS

Table of n, a(n) for n=0..66.


FORMULA

Triangle, odd columns of Pascal's triangle; (1, 0, 0, 0,...) as even columns k.
Alternatively, (since A178616 + A162169  Identity matrix) = Pascal's triangle,
we can begin with Pascal's triangle, subtract A162169, then add the Identity
matrix to obtain A178616.


EXAMPLE

First few rows of the triangle =
1,
0, 1;
0, 2, 1;
0, 3, 0, 1
0, 4, 0, 4, 1;
0, 5, 0, 10, 0, 1;
0, 6, 0, 20, 0, 6, 1;
0, 7, 0, 35, 0, 21, 0, 1;
0, 8, 0, 56, 0, 56, 0 8, 1;
0, 9, 0, 84, 0, 126, 0, 36, 0, 1;
0, 10, 0, 120, 0, 252, 0, 120, 0, 10, 1;
0, 11, 0, 165, 0, 462, 0, 330, 0, 55, 0, 1;
...


CROSSREFS

Cf. A162109, A065619, A052950, A095704.
Sequence in context: A159813 A157409 A245960 * A165252 A127373 A200123
Adjacent sequences: A178613 A178614 A178615 * A178617 A178618 A178619


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, May 30 2010


STATUS

approved



