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A157392 A partition product of Stirling_1 type [parameter k = 2] with biggest-part statistic (triangle read by rows).

%I A157392 #2 Mar 30 2012 17:27:11
%S A157392 1,1,2,1,6,2,1,24,8,0,1,80,60,0,0,1,330,320,0,0,0,1,1302,2030,0,0,0,0,
%T A157392 1,5936,12432,0,0,0,0,0,1,26784,81368,0,0,0,0,0,0,1,133650,545120,0,0,
%U A157392 0,0,0,0,0,1,669350,3825690
%N A157392 A partition product of Stirling_1 type [parameter k = 2] with biggest-part statistic (triangle read by rows).
%C A157392 Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = 2,
%C A157392 summed over parts with equal biggest part (see the Luschny link).
%C A157392 Underlying partition triangle is A144358.
%C A157392 Same partition product with length statistic is A049404.
%C A157392 Diagonal a(A000217(n)) = falling_factorial(2,n-1), row in A008279
%C A157392 Row sum is A049425.
%H A157392 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157392 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling1partitions.html"> Generalized Stirling_1 Triangles</a>.
%F A157392 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157392 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157392 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157392 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = = product_{j=0..n-2}(j-n+4).
%Y A157392 Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395
%K A157392 easy,nonn,tabl
%O A157392 1,3
%A A157392 _Peter Luschny_, Mar 07 2009, Mar 14 2009