

A157402


A partition product of Stirling_2 type [parameter k = 2] with biggestpart statistic (triangle read by rows).


10



1, 1, 2, 1, 6, 10, 1, 24, 40, 80, 1, 80, 300, 400, 880, 1, 330, 2400, 3600, 5280, 12320, 1, 1302, 15750, 47600, 55440, 86240, 209440, 1, 5936, 129360, 588000, 837760, 1034880, 1675520, 4188800, 1, 26784, 1146040, 5856480
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OFFSET

1,3


COMMENTS

Partition product of prod_{j=0..n1}((k + 1)*j  1) and n! at k = 2,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A143172.
Same partition product with length statistic is A004747.
Diagonal a(A000217) = A008544.
Row sum is A015735.


LINKS

Table of n, a(n) for n=1..40.
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..n1}(3*j  1).


CROSSREFS

Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157403, A157404, A157405
Sequence in context: A025252 A177863 A193601 * A069114 A173773 A305512
Adjacent sequences: A157399 A157400 A157401 * A157403 A157404 A157405


KEYWORD

easy,nonn,tabl


AUTHOR

Peter Luschny, Mar 09 2009, Mar 14 2009


STATUS

approved



