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A157386 A partition product of Stirling_1 type [parameter k = -6] with biggest-part statistic (triangle read by rows).

%I A157386 #2 Mar 30 2012 17:27:11
%S A157386 1,1,6,1,18,42,1,144,168,336,1,600,2940,1680,3024,1,4950,33600,35280,
%T A157386 18144,30240,1,26586,336630,717360,444528,211680,332640,1,234528,
%U A157386 4870992,11313120,10329984,5927040,2661120,3991680
%N A157386 A partition product of Stirling_1 type [parameter k = -6] with biggest-part statistic (triangle read by rows).
%C A157386 Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = -6,
%C A157386 summed over parts with equal biggest part (see the Luschny link).
%C A157386 Underlying partition triangle is A144356.
%C A157386 Same partition product with length statistic is A049374.
%C A157386 Diagonal a(A000217(n)) = rising_factorial(6,n-1), A001725(n+4).
%C A157386 Row sum is A049402.
%H A157386 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157386 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling1partitions.html"> Generalized Stirling_1 Triangles</a>.
%F A157386 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157386 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157386 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157386 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-2}(j-n-4).
%Y A157386 Cf. A157385, A157384, A157383, A157400, A126074, A157391, A157392, A157393, A157394, A157395
%K A157386 easy,nonn,tabl
%O A157386 1,3
%A A157386 _Peter Luschny_, Mar 07 2009, Mar 14 2009