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A157405
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A partition product of Stirling_2 type [parameter k = 5] with biggest-part statistic (triangle read by rows).
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10
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1, 1, 5, 1, 15, 55, 1, 105, 220, 935, 1, 425, 3300, 4675, 21505, 1, 3075, 47850, 84150, 129030, 623645, 1, 15855, 415800, 2323475, 2709630, 4365515, 415800, 2323475, 2709630, 4365515, 21827575, 1, 123515, 6394080, 51934575
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 5,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A144268.
Same partition product with length statistic is A013988.
Diagonal a(A000217) = A008543.
Row sum is A028844.
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LINKS
| Peter Luschny, Counting with Partitions.
Peter Luschny, Generalized Stirling_2 Triangles.
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FORMULA
| T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(6*j - 1).
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CROSSREFS
| Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404
Sequence in context: A157395 A157385 A157397 * A019429 A093826 A144699
Adjacent sequences: A157402 A157403 A157404 * A157406 A157407 A157408
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Mar 09 2009, Mar 14 2009
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