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Search: id:A157393
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| A157393 |
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A partition product of Stirling_1 type [parameter k = 3] with biggest-part statistic (triangle read by rows). |
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+0
11
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| 1, 1, 3, 1, 9, 6, 1, 45, 24, 6, 1, 165, 240, 30, 0, 1, 855, 1560, 360, 0, 0, 1, 3843, 12180, 3360, 0, 0, 0, 1, 21819, 96096, 30660, 0, 0, 0, 0, 1, 114075, 794304, 318276, 0, 0, 0, 0, 0, 1, 703215, 6850080, 3270960, 0, 0, 0, 0, 0, 0, 1, 4125495, 62516520, 35053920, 0, 0
(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 prod_{j=0..n-2}(k-n+j+2) and n! at k = 3,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A144877.
Same partition product with length statistic is A049410.
Diagonal a(A000217(n)) = falling_factorial(3,n-1), row in A008279
Row sum is A049426.
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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+5).
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CROSSREFS
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Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395
Sequence in context: A105545 A164942 A027465 this_sequence A127552 A052931 A006803
Adjacent sequences: A157390 A157391 A157392 this_sequence A157394 A157395 A157396
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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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