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A157397 A partition product of Stirling_2 type [parameter k = -5] with biggest-part statistic (triangle read by rows). 10
1, 1, 5, 1, 15, 45, 1, 105, 180, 585, 1, 425, 2700, 2925, 9945, 1, 3075, 34650, 52650, 59670, 208845, 1, 15855, 308700, 1248975, 1253070, 1461915, 5221125, 1, 123515, 4475520, 23689575, 33972120, 35085960, 41769000 (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 = -5,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A134273.
Same partition product with length statistic is A049029.
Diagonal a(A000217) = A007696.
Row sum is A049120.
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}(-4*j - 1).
CROSSREFS
Sequence in context: A264616 A157395 A157385 * A157405 A283434 A019429
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 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)