

A140822


Triangle t(n,m) = binomial(n,gcd(n,m)) read by rows, 0<=m<=n.


0



1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 5, 5, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 8, 28, 8, 70, 8, 28, 8, 1, 1, 9, 9, 84, 9, 9, 84, 9, 9, 1, 1, 10, 45, 10, 45, 252, 45, 10, 45, 10, 1
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OFFSET

0,5


COMMENTS

Row sums are 1, 2, 4, 8, 16, 22, 64, 44, 160, 224, 474,...


LINKS

Table of n, a(n) for n=0..65.


FORMULA

t(n,m) = A007318(n,A109004(n,m)).


EXAMPLE

1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 4, 6, 4, 1;
1, 5, 5, 5, 5, 1;
1, 6, 15, 20, 15, 6, 1;
1, 7, 7, 7, 7, 7, 7, 1;
1, 8, 28, 8, 70, 8, 28, 8, 1;
1, 9, 9, 84, 9, 9, 84, 9, 9, 1;
1, 10, 45, 10, 45, 252, 45, 10, 45, 10, 1;


MATHEMATICA

a = Table[Table[Binomial[n, GCD[n, m]], {m, 0, n}], {n, 0, 10}]; Flatten[a]


CROSSREFS

Sequence in context: A034930 A095142 A180171 * A212954 A089239 A223968
Adjacent sequences: A140819 A140820 A140821 * A140823 A140824 A140825


KEYWORD

nonn,easy,tabl


AUTHOR

Roger L. Bagula and Gary W. Adamson, Jul 16 2008


EXTENSIONS

Offset corrected.  R. J. Mathar, Nov 07 2011


STATUS

approved



