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A157399 A partition product of Stirling_2 type [parameter k = -3] with biggest-part statistic (triangle read by rows).

%I A157399 #2 Mar 30 2012 17:27:11
%S A157399 1,1,3,1,9,15,1,45,60,105,1,165,600,525,945,1,855,5250,6300,5670,
%T A157399 10395,1,3843,39900,91875,79380,72765,135135,1,21819,391440,1164975,
%U A157399 1323000,1164240,1081080,2027025,1
%N A157399 A partition product of Stirling_2 type [parameter k = -3] with biggest-part statistic (triangle read by rows).
%C A157399 Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = -3,
%C A157399 summed over parts with equal biggest part (see the Luschny link).
%C A157399 Underlying partition triangle is A134144.
%C A157399 Same partition product with length statistic is A035342.
%C A157399 Diagonal a(A000217) = A001147.
%C A157399 Row sum is A049118.
%H A157399 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157399 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.
%F A157399 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157399 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157399 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157399 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(-2*j - 1).
%Y A157399 Cf. A157396, A157397, A157398, A157400, A080510, A157401, A157402, A157403, A157404, A157405
%K A157399 easy,nonn,tabl
%O A157399 1,3
%A A157399 _Peter Luschny_, Mar 09 2009, Mar 14 2009