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A157384 A partition product of Stirling_1 type [parameter k = -4] with biggest-part statistic (triangle read by rows).

%I A157384 #2 Mar 30 2012 17:27:11
%S A157384 1,1,4,1,12,20,1,72,80,120,1,280,1000,600,840,1,1740,9200,9000,5040,
%T A157384 6720,1,8484,79100,138600,88200,47040,60480,1,57232,874720,1789200,
%U A157384 1552320,940800,483840,604800,1,328752,9532880
%N A157384 A partition product of Stirling_1 type [parameter k = -4] with biggest-part statistic (triangle read by rows).
%C A157384 Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = -4,
%C A157384 summed over parts with equal biggest part (see the Luschny link).
%C A157384 Underlying partition triangle is A144354.
%C A157384 Same partition product with length statistic is A049352.
%C A157384 Diagonal a(A000217(n)) = rising_factorial(4,n-1), A001715(n+2).
%C A157384 Row sum is A049377.
%H A157384 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157384 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling1partitions.html"> Generalized Stirling_1 Triangles</a>.
%F A157384 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157384 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157384 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157384 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-2}(j-n-2).
%Y A157384 Cf. A157386, A157384, A157383, A157400, A126074, A157391, A157392, A157393, A157394, A157395
%K A157384 easy,nonn,tabl
%O A157384 1,3
%A A157384 _Peter Luschny_, Mar 07 2009, Mar 14 2009