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A157392
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A partition product of Stirling_1 type [parameter k = 2] with biggest-part statistic (triangle read by rows).
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11
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1, 1, 2, 1, 6, 2, 1, 24, 8, 0, 1, 80, 60, 0, 0, 1, 330, 320, 0, 0, 0, 1, 1302, 2030, 0, 0, 0, 0, 1, 5936, 12432, 0, 0, 0, 0, 0, 1, 26784, 81368, 0, 0, 0, 0, 0, 0, 1, 133650, 545120, 0, 0, 0, 0, 0, 0, 0, 1, 669350, 3825690
(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-2}(k-n+j+2) and n! at k = 2,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A144358.
Same partition product with length statistic is A049404.
Diagonal a(A000217(n)) = falling_factorial(2,n-1), row in A008279
Row sum is A049425.
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LINKS
| Peter Luschny, Counting with Partitions.
Peter Luschny, Generalized Stirling_1 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-2}(j-n+4).
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CROSSREFS
| Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395
Sequence in context: A179863 A069123 A134133 * A134134 A198870 A050457
Adjacent sequences: A157389 A157390 A157391 * A157393 A157394 A157395
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Mar 07 2009, Mar 14 2009
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