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A157395 A partition product of Stirling_1 type [parameter k = 5] with biggest-part statistic (triangle read by rows).

%I A157395 #2 Mar 30 2012 17:27:11
%S A157395 1,1,5,1,15,20,1,105,80,60,1,425,1200,300,120,1,3075,10400,5400,720,
%T A157395 120,1,15855,102200,75600,15120,840,0,1,123515,1149120,907200,241920,
%U A157395 20160,0,0,1,757755,12783680,13426560,3719520,362880
%N A157395 A partition product of Stirling_1 type [parameter k = 5] with biggest-part statistic (triangle read by rows).
%C A157395 Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = 5,
%C A157395 summed over parts with equal biggest part (see the Luschny link).
%C A157395 Underlying partition triangle is A144879.
%C A157395 Same partition product with length statistic is A049411.
%C A157395 Diagonal a(A000217(n)) = falling_factorial(5,n-1), row in A008279
%C A157395 Row sum is A049428.
%H A157395 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157395 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling1partitions.html"> Generalized Stirling_1 Triangles</a>.
%F A157395 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157395 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157395 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157395 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-2}(j-n+7).
%Y A157395 Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395
%K A157395 easy,nonn,tabl
%O A157395 1,3
%A A157395 _Peter Luschny_, Mar 07 2009, Mar 14 2009