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 A157397 A partition product of Stirling_2 type [parameter k = -5] with biggest-part statistic (triangle read by rows). 10

%I

%S 1,1,5,1,15,45,1,105,180,585,1,425,2700,2925,9945,1,3075,34650,52650,

%T 59670,208845,1,15855,308700,1248975,1253070,1461915,5221125,1,123515,

%U 4475520,23689575,33972120,35085960,41769000

%N A partition product of Stirling_2 type [parameter k = -5] with biggest-part statistic (triangle read by rows).

%C Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = -5,

%C summed over parts with equal biggest part (see the Luschny link).

%C Underlying partition triangle is A134273.

%C Same partition product with length statistic is A049029.

%C Diagonal a(A000217) = A007696.

%C Row sum is A049120.

%H Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.

%H Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.

%F T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n

%F T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that

%F 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),

%F f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(-4*j - 1).

%Y Cf. A157396, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405

%K easy,nonn,tabl

%O 1,3

%A _Peter Luschny_, Mar 09 2009

%E Offset corrected by _Peter Luschny_, Mar 14 2009

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