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Search: id:A157385
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| A157385 |
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A partition product of Stirling_1 type [parameter k = -5] with biggest-part statistic (triangle read by rows). |
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+0
10
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| 1, 1, 5, 1, 15, 30, 1, 105, 120, 210, 1, 425, 1800, 1050, 1680, 1, 3075, 18600, 18900, 10080, 15120, 1, 15855, 174300, 338100, 211680, 105840, 151200, 1, 123515, 2227680, 4865700, 4327680, 2540160, 1209600, 1663200, 1, 757755
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = -5,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A144355.
Same partition product with length statistic is A049353.
Diagonal a(A000217(n)) = rising_factorial(5,n-1), A001720(n+3).
Row sum is A049378.
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LINKS
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Peter Luschny, Counting with Partitions.
Peter Luschny, Generalized Stirling_1 Triangles.
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FORMULA
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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-2}(j-n-3).
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CROSSREFS
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Cf. A157386, A157384, A157383, A157400, A126074, A157391, A157392, A157393, A157394, A157395
Sequence in context: A087727 A039807 A157395 this_sequence A157397 A157405 A019429
Adjacent sequences: A157382 A157383 A157384 this_sequence A157386 A157387 A157388
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Mar 07 2009, Mar 14 2009
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