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A157384
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A partition product of Stirling_1 type [parameter k = -4] with biggest-part statistic (triangle read by rows).
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11
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1, 1, 4, 1, 12, 20, 1, 72, 80, 120, 1, 280, 1000, 600, 840, 1, 1740, 9200, 9000, 5040, 6720, 1, 8484, 79100, 138600, 88200, 47040, 60480, 1, 57232, 874720, 1789200, 1552320, 940800, 483840, 604800, 1, 328752, 9532880
(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 = -4,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A144354.
Same partition product with length statistic is A049352.
Diagonal a(A000217(n)) = rising_factorial(4,n-1), A001715(n+2).
Row sum is A049377.
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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-2).
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CROSSREFS
| Cf. A157386, A157384, A157383, A157400, A126074, A157391, A157392, A157393, A157394, A157395
Sequence in context: A078219 A187541 A117413 * A173621 A105197 A157398
Adjacent sequences: A157381 A157382 A157383 * A157385 A157386 A157387
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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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