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A172479 Triangle read by rows: T(n,k) = A152827(n)/(A152827(k)* A152827(n-k)) where A152827 are the partial products of A000009. 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

A generalized binomial coefficient associated with the partitions into distinct parts (A000009).

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 * A122085 A209612 A209805

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 February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)