A082904 Triangle read by rows: Pascal's triangle restricted to binomial(n, d) where d is a divisor of n.

1, 2, 1, 3, 1, 4, 6, 1, 5, 1, 6, 15, 20, 1, 7, 1, 8, 28, 70, 1, 9, 84, 1, 10, 45, 252, 1, 11, 1, 12, 66, 220, 495, 924, 1, 13, 1, 14, 91, 3432, 1, 15, 455, 3003, 1, 16, 120, 1820, 12870, 1, 17, 1, 18, 153, 816, 18564, 48620, 1, 19, 1, 20, 190, 4845, 15504, 184756, 1, 21, 1330

Offset

0,2

Links

Table of n, a(n) for n=0..67.

Example

n-th row of table consists of A000005(n) terms:
   1;
   2,   1;
   3,   1;
   4,   6,   1;
   5,   1;
   6,  15,  20,   1;
   7,   1;
   8,  28,  70,   1;
   9,  84,   1;
  10,  45, 252,   1;
  ...
25th row = {C(25,1), C(25,5), C(25,25)} = {25, 53130, 1}.

Maple

A082904_row := proc(n) seq(binomial(n, d), d=numtheory[divisors](n)) end:
seq(print(A082904_row(n)), n=1..10); # Peter Luschny, Dec 06 2011

Mathematica

Flatten[Table[Binomial[n, Divisors[n]], {n, 1, 25}], 1]

Prog

(PARI) for(n=1, 30, fordiv(n, d, print1(binomial(n, d)", "))) \\ Charles R Greathouse IV, Dec 06 2011

Crossrefs

Cf. A000005, A007318, A056045.

Sequence in context: A293892 A295885 A329035 * A034868 A050382 A197956

Adjacent sequences: A082901 A082902 A082903 * A082905 A082906 A082907

Keyword

nonn,tabf

Author

Labos Elemer, Apr 23 2003

Extensions

New name from Peter Luschny, Dec 06 2011

Status

approved