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A157398 A partition product of Stirling_2 type [parameter k = -4] with biggest-part statistic (triangle read by rows).

%I A157398 #2 Mar 30 2012 17:27:11
%S A157398 1,1,4,1,12,28,1,72,112,280,1,280,1400,1400,3640,1,1740,15120,21000,
%T A157398 21840,58240,1,8484,126420,401800,382200,407680,1106560,1,57232,
%U A157398 1538208,6370000,8357440,8153600,8852480,24344320,1
%N A157398 A partition product of Stirling_2 type [parameter k = -4] with biggest-part statistic (triangle read by rows).
%C A157398 Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = -4,
%C A157398 summed over parts with equal biggest part (see the Luschny link).
%C A157398 Underlying partition triangle is A134149.
%C A157398 Same partition product with length statistic is A035469.
%C A157398 Diagonal a(A000217) = A007559.
%C A157398 Row sum is A049119.
%H A157398 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157398 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.
%F A157398 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157398 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157398 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157398 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(-3*j - 1).
%Y A157398 Cf. A157396, A157397, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405
%K A157398 easy,nonn,tabl
%O A157398 1,3
%A A157398 _Peter Luschny_, Mar 09 2009, Mar 14 2009