|
Search: id:A157396
|
|
|
| A157396 |
|
A partition product of Stirling_2 type [parameter k = -6] with biggest-part statistic (triangle read by rows). |
|
+0
11
|
|
| 1, 1, 6, 1, 18, 66, 1, 144, 264, 1056, 1, 600, 4620, 5280, 22176, 1, 4950, 68640, 110880, 133056, 576576, 1, 26586, 639870, 3141600, 3259872, 4036032, 17873856, 1, 234528, 10759056, 69263040, 105557760, 113008896, 142990848
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = -6,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A134278.
Same partition product with length statistic is A049385.
Diagonal a(A000217) = A008548.
Row sum is A049412.
|
|
LINKS
|
Peter Luschny, Counting with Partitions.
Peter Luschny, Generalized Stirling_2 Triangles.
|
|
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}(-5*j - 1).
|
|
CROSSREFS
|
Cf. A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405
Sequence in context: A049325 A092371 A157386 this_sequence A019430 A064083 A152249
Adjacent sequences: A157393 A157394 A157395 this_sequence A157397 A157398 A157399
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Peter Luschny (peter(AT)luschny.de), Mar 09 2009
|
|
EXTENSIONS
|
Offset corrected by Peter Luschny (peter(AT)luschny.de), Mar 14 2009
|
|
|
Search completed in 0.002 seconds
|
