A081418 A000720 applied to Pascal-triangle as follows: C(Pi[n],Pi[j])], j,0..n and n=0,1,2,...

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

Offset

0,9

Links

Table of n, a(n) for n=0..98.

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

Cf. A000720, A081417.

Sequence in context: A177991 A146289 A214575 * A088951 A361633 A186006

Adjacent sequences: A081415 A081416 A081417 * A081419 A081420 A081421

Keyword

nonn,tabl

Author

Labos Elemer, Apr 02 2003

Status

approved