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A082904
Triangle read by rows: Pascal's triangle restricted to binomial(n, d) where d is a divisor of n.
0
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
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
KEYWORD
nonn,tabf
AUTHOR
Labos Elemer, Apr 23 2003
EXTENSIONS
New name from Peter Luschny, Dec 06 2011
STATUS
approved