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A157391
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A partition product of Stirling_1 type [parameter k = 1] with biggest-part statistic (triangle read by rows).
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11
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1, 1, 1, 1, 3, 0, 1, 9, 0, 0, 1, 25, 0, 0, 0, 1, 75, 0, 0, 0, 0, 1, 231, 0, 0, 0, 0, 0, 1, 763, 0, 0, 0, 0, 0, 0, 1, 2619, 0, 0, 0, 0, 0, 0, 0, 1, 9495, 0, 0, 0, 0, 0, 0, 0, 0, 1, 35695, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 140151
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = 1,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A144357.
Same partition product with length statistic is A049403.
Diagonal a(A000217(n)) = falling_factorial(1,n-1), row in A008279.
Row sum is A000085.
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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+3).
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CROSSREFS
| Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395
Sequence in context: A011074 A020816 A174860 * A099097 A152150 A136239
Adjacent sequences: A157388 A157389 A157390 * A157392 A157393 A157394
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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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