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A157385 A partition product of Stirling_1 type [parameter k = -5] with biggest-part statistic (triangle read by rows).

%I A157385 #2 Mar 30 2012 17:27:11
%S A157385 1,1,5,1,15,30,1,105,120,210,1,425,1800,1050,1680,1,3075,18600,18900,
%T A157385 10080,15120,1,15855,174300,338100,211680,105840,151200,1,123515,
%U A157385 2227680,4865700,4327680,2540160,1209600,1663200,1,757755
%N A157385 A partition product of Stirling_1 type [parameter k = -5] with biggest-part statistic (triangle read by rows).
%C A157385 Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = -5,
%C A157385 summed over parts with equal biggest part (see the Luschny link).
%C A157385 Underlying partition triangle is A144355.
%C A157385 Same partition product with length statistic is A049353.
%C A157385 Diagonal a(A000217(n)) = rising_factorial(5,n-1), A001720(n+3).
%C A157385 Row sum is A049378.
%H A157385 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157385 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling1partitions.html"> Generalized Stirling_1 Triangles</a>.
%F A157385 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157385 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157385 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157385 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-2}(j-n-3).
%Y A157385 Cf. A157386, A157384, A157383, A157400, A126074, A157391, A157392, A157393, A157394, A157395
%K A157385 easy,nonn,tabl
%O A157385 1,3
%A A157385 _Peter Luschny_, Mar 07 2009, Mar 14 2009