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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 Table of n, a(n) for n=0..65. 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 Cf. A000009, A152827. Sequence in context: A088855 A034851 A172453 * A339788 A122085 A209612 Adjacent sequences: A172476 A172477 A172478 * A172480 A172481 A172482 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.)