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A157400
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A partition product with biggest-part statistic of Stirling_1 type (with parameter k = -2) as well as of Stirling_2 type (with parameter k = -2), (triangle read by rows).
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20
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1, 1, 2, 1, 6, 6, 1, 24, 24, 24, 1, 80, 180, 120, 120, 1, 330, 1200, 1080, 720, 720, 1, 1302, 7770, 10920, 7560, 5040, 5040, 1, 5936, 57456, 102480, 87360, 60480, 40320, 40320
(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-1}((k+1)*j - 1) and n! at k = -2, summed
over parts with equal biggest part (Stirling_2 type) as well as partition
product of prod_{j=0..n-2}(k-n+j+2) and n! at k = -2 (Stirling_1 type).
It shares this property with the signless Lah numbers.
Underlying partition triangle is A130561.
Same partition product with length statistic is A105278.
Diagonal a(A000217) = A000142.
Row sum is A000262.
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LINKS
| Peter Luschny, Counting with Partitions.
Peter Luschny, Generalized Stirling_1 Triangles.
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}(-j-1)
OR f_n = product_{j=0..n-2}(j-n) since both have the same absolute value n!.
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CROSSREFS
| Cf. A157396, A157397, A157398, A157399, A080510, A157401, A157402, A157403, A157404, A157405, A157386, A157385, A157384, A157383, A126074, A157391, A157392, A157393, A157394, A157395
Sequence in context: A110183 A110098 A130561 * A091599 A048999 A066667
Adjacent sequences: A157397 A157398 A157399 * A157401 A157402 A157403
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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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