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A157395
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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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11
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1, 1, 5, 1, 15, 20, 1, 105, 80, 60, 1, 425, 1200, 300, 120, 1, 3075, 10400, 5400, 720, 120, 1, 15855, 102200, 75600, 15120, 840, 0, 1, 123515, 1149120, 907200, 241920, 20160, 0, 0, 1, 757755, 12783680, 13426560, 3719520, 362880
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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 A144879.
Same partition product with length statistic is A049411.
Diagonal a(A000217(n)) = falling_factorial(5,n-1), row in A008279
Row sum is A049428.
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LINKS
| Peter Luschny, Counting with Partitions.
Peter Luschny, Generalized Stirling_1 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-2}(j-n+7).
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CROSSREFS
| Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395
Sequence in context: A087727 A039807 A185263 * A157385 A157397 A157405
Adjacent sequences: A157392 A157393 A157394 * A157396 A157397 A157398
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Mar 07 2009, Mar 14 2009
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