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A157405 A partition product of Stirling_2 type [parameter k = 5] with biggest-part statistic (triangle read by rows).

%I A157405 #2 Mar 30 2012 17:27:11
%S A157405 1,1,5,1,15,55,1,105,220,935,1,425,3300,4675,21505,1,3075,47850,84150,
%T A157405 129030,623645,1,15855,415800,2323475,2709630,4365515,415800,2323475,
%U A157405 2709630,4365515,21827575,1,123515,6394080,51934575
%N A157405 A partition product of Stirling_2 type [parameter k = 5] with biggest-part statistic (triangle read by rows).
%C A157405 Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 5,
%C A157405 summed over parts with equal biggest part (see the Luschny link).
%C A157405 Underlying partition triangle is A144268.
%C A157405 Same partition product with length statistic is A013988.
%C A157405 Diagonal a(A000217) = A008543.
%C A157405 Row sum is A028844.
%H A157405 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157405 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.
%F A157405 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157405 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157405 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157405 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(6*j - 1).
%Y A157405 Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404
%K A157405 easy,nonn,tabl
%O A157405 0,3
%A A157405 _Peter Luschny_, Mar 09 2009, Mar 14 2009