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A145520
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Triangle read by rows: T2[n,k] = Sum_{partitions of n with k parts p(n, k; m_1, m_2, m_3, ..., m_n)} c(n; m_1, m_2, ..., m_n) * x_1^m_1 * x_2^m_2 * ... x^n*m_n, where x_i = i-th prime.
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1
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2, 3, 4, 5, 18, 8, 7, 67, 72, 16, 11, 220, 470, 240, 32, 13, 697, 2625, 2420, 720, 64, 17, 2100, 13559, 20230, 10360, 2016, 128, 19, 6159, 66374, 152313, 120400, 39200, 5376, 256, 23, 17340, 313136, 1071168, 1235346, 602784, 135744, 13824, 512, 29, 47581
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Here c(n; m_1, m_2, ..., m_n) = n! / (m_1!*1!^m_1 * m_2!*2!^m_2 * ... * m_n!*n!^m_n) is the number of ways to realize the partition p(n, k; m_1, m_2, m_3, ..., m_n).
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LINKS
| Tilman Neumann, More terms, partitions generator and transform implementation
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CROSSREFS
| Cf. A000040, A007446 (row sums), A145518
Sequence in context: A117885 A030574 A162657 * A061412 A165646 A024635
Adjacent sequences: A145517 A145518 A145519 * A145521 A145522 A145523
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KEYWORD
| nonn,tabl
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AUTHOR
| Tilman Neumann (Tilman.Neumann(AT)web.de), Oct 12 2008, Oct 13 2008, Sep 02 2009
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