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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

Table of n, a(n) for n=1..45.

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}(2*j - 1).

CROSSREFS

Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157402, A157403, A157404, A157405

Sequence in context: A122919 A188513 A216916 * A143911 A185422 A131889

Adjacent sequences:  A157398 A157399 A157400 * A157402 A157403 A157404

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Luschny, Mar 09 2009, Mar 14 2009

STATUS

approved

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Last modified October 22 19:18 EDT 2014. Contains 248400 sequences.