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A157401
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A partition product of Stirling_2 type [parameter k = 1] with biggest-part statistic (triangle read by rows).
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10
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1, 1, 1, 1, 1, 3, 3, 1, 9, 12, 15, 1, 25, 60, 75, 105, 1, 75, 330, 450, 630, 945, 1, 231, 1680, 3675, 4410, 6615, 10395, 1, 763, 9408, 30975, 41160, 52920, 83160, 135135, 1, 2619, 56952, 233415, 489510, 555660, 748440, 1216215
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 1,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A143171.
Same partition product with length statistic is A001497.
Diagonal a(A000217) = A001147.
Row sum is A001515.
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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}(2*j - 1).
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CROSSREFS
| Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157402, A157403, A157404, A157405
Sequence in context: A084145 A122919 A188513 * A143911 A185422 A131889
Adjacent sequences: A157398 A157399 A157400 * A157402 A157403 A157404
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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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