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A157397
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A partition product of Stirling_2 type [parameter k = -5] with biggest-part statistic (triangle read by rows).
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10
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1, 1, 5, 1, 15, 45, 1, 105, 180, 585, 1, 425, 2700, 2925, 9945, 1, 3075, 34650, 52650, 59670, 208845, 1, 15855, 308700, 1248975, 1253070, 1461915, 5221125, 1, 123515, 4475520, 23689575, 33972120, 35085960, 41769000
(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 = -5,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A134273.
Same partition product with length statistic is A049029.
Diagonal a(A000217) = A007696.
Row sum is A049120.
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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}(-4*j - 1).
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CROSSREFS
| Cf. A157396, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405
Sequence in context: A185263 A157395 A157385 * A157405 A019429 A093826
Adjacent sequences: A157394 A157395 A157396 * A157398 A157399 A157400
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Mar 09 2009
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EXTENSIONS
| Offset corrected by Peter Luschny (peter(AT)luschny.de), Mar 14 2009
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