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A157396 A partition product of Stirling_2 type [parameter k = -6] with biggest-part statistic (triangle read by rows).

%I A157396 #2 Mar 30 2012 17:27:11
%S A157396 1,1,6,1,18,66,1,144,264,1056,1,600,4620,5280,22176,1,4950,68640,
%T A157396 110880,133056,576576,1,26586,639870,3141600,3259872,4036032,17873856,
%U A157396 1,234528,10759056,69263040,105557760,113008896,142990848
%N A157396 A partition product of Stirling_2 type [parameter k = -6] with biggest-part statistic (triangle read by rows).
%C A157396 Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = -6,
%C A157396 summed over parts with equal biggest part (see the Luschny link).
%C A157396 Underlying partition triangle is A134278.
%C A157396 Same partition product with length statistic is A049385.
%C A157396 Diagonal a(A000217) = A008548.
%C A157396 Row sum is A049412.
%H A157396 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157396 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.
%F A157396 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157396 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157396 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157396 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(-5*j - 1).
%Y A157396 Cf. A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405
%K A157396 easy,nonn,tabl
%O A157396 1,3
%A A157396 _Peter Luschny_, Mar 09 2009
%E A157396 Offset corrected by _Peter Luschny_, Mar 14 2009