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A157396 A partition product of Stirling_2 type [parameter k = -6] with biggest-part statistic (triangle read by rows). 10
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; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
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
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
Sequence in context: A092371 A187552 A157386 * A019430 A064083 A152249
KEYWORD
easy,nonn,tabl
AUTHOR
Peter Luschny, Mar 09 2009
EXTENSIONS
Offset corrected by Peter Luschny, Mar 14 2009
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)