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A172479 Triangle read by rows: T(n,k) = A152827(n)/(A152827(k)* A152827(n-k)). 0
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 3, 6, 6, 3, 1, 1, 4, 12, 12, 12, 4, 1, 1, 5, 20, 30, 30, 20, 5, 1, 1, 6, 30, 60, 90, 60, 30, 6, 1, 1, 8, 48, 120, 240, 240, 120, 48, 8, 1, 1, 10, 80, 240, 600, 800, 600, 240, 80, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
Row sums are 1, 2, 3, 6, 10, 20, 46, 112, 284, 834, 2662, ... .
LINKS
Donald E. Knuth and Herbert S. Wilf, The power of a prime that divides a generalized binomial coefficient, J. Reine Angew. Math., 396:212-219, 1989.
FORMULA
T(n,k) = A152827(n)/(A152827(k)* A152827(n-k)).
T(n,k) = Product_{i=1..n} A000009(i)/(Product_{i=1..k} A000009(i)*Product_{i=1..n-k} A000009(i)).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 2, 4, 2, 1;
1, 3, 6, 6, 3, 1;
1, 4, 12, 12, 12, 4, 1;
1, 5, 20, 30, 30, 20, 5, 1;
1, 6, 30, 60, 90, 60, 30, 6, 1;
1, 8, 48, 120, 240, 240, 120, 48, 8, 1;
1, 10, 80, 240, 600, 800, 600, 240, 80, 10, 1;
MATHEMATICA
c[n_] := Product[PartitionsQ[m], {m, 1, n}];
t[n_, m_] := c[n]/(c[m]*c[n - m]);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
CROSSREFS
Sequence in context: A088855 A034851 A172453 * A339788 A122085 A209612
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 04 2010
EXTENSIONS
New name and edits by Tom Edgar, Jan 23 2015
STATUS
approved

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Last modified July 23 11:07 EDT 2024. Contains 374549 sequences. (Running on oeis4.)