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A157397 A partition product of Stirling_2 type [parameter k = -5] with biggest-part statistic (triangle read by rows).

%I A157397 #2 Mar 30 2012 17:27:11
%S A157397 1,1,5,1,15,45,1,105,180,585,1,425,2700,2925,9945,1,3075,34650,52650,
%T A157397 59670,208845,1,15855,308700,1248975,1253070,1461915,5221125,1,123515,
%U A157397 4475520,23689575,33972120,35085960,41769000
%N A157397 A partition product of Stirling_2 type [parameter k = -5] with biggest-part statistic (triangle read by rows).
%C A157397 Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = -5,
%C A157397 summed over parts with equal biggest part (see the Luschny link).
%C A157397 Underlying partition triangle is A134273.
%C A157397 Same partition product with length statistic is A049029.
%C A157397 Diagonal a(A000217) = A007696.
%C A157397 Row sum is A049120.
%H A157397 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157397 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.
%F A157397 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157397 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157397 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157397 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(-4*j - 1).
%Y A157397 Cf. A157396, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405
%K A157397 easy,nonn,tabl
%O A157397 1,3
%A A157397 _Peter Luschny_, Mar 09 2009
%E A157397 Offset corrected by _Peter Luschny_, Mar 14 2009