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A081418
A000720 applied to Pascal-triangle as follows: C(pi(n),pi(j)), j=0..n and n=0,1,2,...
0
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 4, 6, 6, 4, 4, 1, 1, 1, 4, 6, 6, 4, 4, 1, 1, 1, 1, 4, 6, 6, 4, 4, 1, 1, 1, 1, 1, 4, 6, 6, 4, 4, 1, 1, 1, 1, 1, 1, 5, 10, 10, 10, 10, 5, 5, 5, 5, 1, 1, 1, 5, 10, 10, 10, 10, 5, 5, 5, 5, 1, 1, 1, 1, 6, 15, 15, 20, 20, 15, 15, 15, 15, 6, 6, 1
OFFSET
0,9
EXAMPLE
Triangle begins:
1,
1,1,
1,1,1,
1,1,2,1,
1,1,2,1,1,
1,1,3,3,3,1,
1,1,3,3,3,1,1,
1,1,4,6,6,4,4,1,
1,1,4,6,6,4,4,1,1,
1,1,4,6,6,4,4,1,1,1,
1,1,4,6,6,4,4,1,1,1,1,
1,1,5,10,10,10,10,5,5,5,5,1,
1,1,5,10,10,10,10,5,5,5,5,1,1,
1,1,6,15,15,20,20,15,15,15,15,6,6,1,
1,1,6,15,15,20,20,15,15,15,15,6,6,1,1,
1,1,6,15,15,20,20,15,15,15,15,6,6,1,1,1
Rows are usually asymmetric; 25th row:
{1,1,9,36,36,84,84,126,126,126,126,126,126,84,84,84,84,36,36,9,9,9,9,1,1,1}
MATHEMATICA
Flatten[Table[Table[Binomial[PrimePi[n], Prime[j]],
{j, 0, n}], {n, 0, 15}], 1]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Labos Elemer, Apr 02 2003
STATUS
approved