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A157404 A partition product of Stirling_2 type [parameter k = 4] with biggest-part statistic (triangle read by rows).

%I A157404 #2 Mar 30 2012 17:27:11
%S A157404 1,1,4,1,12,36,1,72,144,504,1,280,1800,2520,9576,1,1740,22320,37800,
%T A157404 57456,229824,1,8484,182700,864360,1005480,1608768,6664896,1,57232,
%U A157404 2380896,16546320,26276544,32175360,53319168,226606464
%N A157404 A partition product of Stirling_2 type [parameter k = 4] with biggest-part statistic (triangle read by rows).
%C A157404 Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 4,
%C A157404 summed over parts with equal biggest part (see the Luschny link).
%C A157404 Underlying partition triangle is A144267.
%C A157404 Same partition product with length statistic is A011801.
%C A157404 Diagonal a(A000217) = A008546.
%C A157404 Row sum is A028575.
%H A157404 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157404 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.
%F A157404 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157404 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157404 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157404 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(5*j - 1).
%Y A157404 Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157405
%K A157404 easy,nonn,tabl
%O A157404 1,3
%A A157404 _Peter Luschny_, Mar 09 2009