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A098348
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Triangular array read by rows: a(n, k) = number of ordered factorizations of a "hook-type" number with n total prime factors and k distinct prime factors. "Hook-type" means that only one prime can have multiplicity > 1.
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4
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1, 2, 3, 4, 8, 13, 8, 20, 44, 75, 16, 48, 132, 308, 541, 32, 112, 368, 1076, 2612, 4683, 64, 256, 976, 3408, 10404, 25988, 47293, 128, 576, 2496, 10096, 36848, 116180, 296564, 545835, 256, 1280, 6208, 28480, 120400, 454608, 1469892, 3816548
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The first three columns are A000079, A001792 and A098385.
The first two diagonals are A000670 and A005649.
A070175 gives the smallest representative of each hook-type prime signature, so this sequence is a rearrangement of A074206(A070175).
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FORMULA
| a(n, k) = 1+[sum_{i=1..k-1} binomial(k-1, i)*a(i, i)]+[sum_{j=1..k} sum_{i=j..j+n-k-1} binomial(k-1, j-1)*a(i, j)]+[sum_{j=1..k-1} binomial(k-1,j-1)*a(j+n-k, j)]. - David Wasserman (dwasserm(AT)earthlink.net), Feb 21 2008
a(n, k) = A074206(2^(n+1-k)*A070826(k)). - David Wasserman (dwasserm(AT)earthlink.net), Feb 21 2008
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EXAMPLE
| a(4, 2) = 20 because 24=2*2*2*3 has 20 ordered factorizations and so does any other number with the same prime signature.
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CROSSREFS
| Cf. A050324, A070175, A070826, A074206, A095705. A098349 gives the row sums.
Sequence in context: A060200 A057608 A060984 * A131420 A095705 A034776
Adjacent sequences: A098345 A098346 A098347 * A098349 A098350 A098351
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Sep 04 2004
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EXTENSIONS
| Edited and extended by David Wasserman (dwasserm(AT)earthlink.net), Feb 21 2008
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