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A157401 A partition product of Stirling_2 type [parameter k = 1] with biggest-part statistic (triangle read by rows). 10
1, 1, 1, 1, 1, 3, 3, 1, 9, 12, 15, 1, 25, 60, 75, 105, 1, 75, 330, 450, 630, 945, 1, 231, 1680, 3675, 4410, 6615, 10395, 1, 763, 9408, 30975, 41160, 52920, 83160, 135135, 1, 2619, 56952, 233415, 489510, 555660, 748440, 1216215 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 1,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A143171.
Same partition product with length statistic is A001497.
Diagonal a(A000217) = A001147.
Row sum is A001515.
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}(2*j - 1).
CROSSREFS
Sequence in context: A188513 A260301 A216916 * A143911 A185422 A131889
KEYWORD
easy,nonn,tabl
AUTHOR
Peter Luschny, Mar 09 2009, Mar 14 2009
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)