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A091438
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Triangle a(n,k) of partitions of n objects of 2 colors, k of which are black and each part with at least one black object.
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1
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1, 1, 2, 1, 2, 3, 1, 3, 4, 5, 1, 3, 6, 7, 7, 1, 4, 8, 12, 12, 11, 1, 4, 10, 16, 21, 19, 15, 1, 5, 12, 23, 31, 36, 30, 22, 1, 5, 15, 28, 45, 55, 58, 45, 30, 1, 6, 17, 37, 60, 84, 94, 92, 67, 42, 1, 6, 20, 44, 80, 115, 147, 153, 140, 97, 56, 1, 7, 23, 55, 101, 161, 211, 249, 244
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Number of ways to factor p^(n-k)*q^k where p and q are distinct primes and each factor is a multiple of q.
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FORMULA
| G.f.: A(x, y) = prod{i=1..inf, j=1..i}(1/(1-x^i*y^j))
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EXAMPLE
| 1; 1,2; 1,2,3; 1,3,4,5; 1,3,6,7,7; ...
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CROSSREFS
| Row sums: A000219. Main diagonal: A000041. Cf. A054225.
Sequence in context: A066010 A109974 A026820 * A011794 A073300 A104468
Adjacent sequences: A091435 A091436 A091437 * A091439 A091440 A091441
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KEYWORD
| nonn,tabl
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be) and Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004
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