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A157402
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A partition product of Stirling_2 type [parameter k = 2] with biggest-part statistic (triangle read by rows).
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10
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1, 1, 2, 1, 6, 10, 1, 24, 40, 80, 1, 80, 300, 400, 880, 1, 330, 2400, 3600, 5280, 12320, 1, 1302, 15750, 47600, 55440, 86240, 209440, 1, 5936, 129360, 588000, 837760, 1034880, 1675520, 4188800, 1, 26784, 1146040, 5856480
(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 (see the Luschny link).
Underlying partition triangle is A143172.
Same partition product with length statistic is A004747.
Diagonal a(A000217) = A008544.
Row sum is A015735.
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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}(3*j - 1).
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CROSSREFS
| Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157403, A157404, A157405
Sequence in context: A025252 A177863 A193601 * A069114 A173773 A121927
Adjacent sequences: A157399 A157400 A157401 * A157403 A157404 A157405
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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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