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A157405 A partition product of Stirling_2 type [parameter k = 5] with biggest-part statistic (triangle read by rows). 10
1, 1, 5, 1, 15, 55, 1, 105, 220, 935, 1, 425, 3300, 4675, 21505, 1, 3075, 47850, 84150, 129030, 623645, 1, 15855, 415800, 2323475, 2709630, 4365515, 415800, 2323475, 2709630, 4365515, 21827575, 1, 123515, 6394080, 51934575 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 A144268.

Same partition product with length statistic is A013988.

Diagonal a(A000217) = A008543.

Row sum is A028844.

LINKS

Table of n, a(n) for n=0..35.

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}(6*j - 1).

CROSSREFS

Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404

Sequence in context: A157395 A157385 A157397 * A283434 A019429 A221364

Adjacent sequences:  A157402 A157403 A157404 * A157406 A157407 A157408

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Luschny, Mar 09 2009, Mar 14 2009

STATUS

approved

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Last modified September 22 09:45 EDT 2017. Contains 292337 sequences.