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A157402 A partition product of Stirling_2 type [parameter k = 2] with biggest-part statistic (triangle read by rows).

%I A157402 #2 Mar 30 2012 17:27:11
%S A157402 1,1,2,1,6,10,1,24,40,80,1,80,300,400,880,1,330,2400,3600,5280,12320,
%T A157402 1,1302,15750,47600,55440,86240,209440,1,5936,129360,588000,837760,
%U A157402 1034880,1675520,4188800,1,26784,1146040,5856480
%N A157402 A partition product of Stirling_2 type [parameter k = 2] with biggest-part statistic (triangle read by rows).
%C A157402 Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 2,
%C A157402 summed over parts with equal biggest part (see the Luschny link).
%C A157402 Underlying partition triangle is A143172.
%C A157402 Same partition product with length statistic is A004747.
%C A157402 Diagonal a(A000217) = A008544.
%C A157402 Row sum is A015735.
%H A157402 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157402 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.
%F A157402 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157402 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157402 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157402 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(3*j - 1).
%Y A157402 Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157403, A157404, A157405
%K A157402 easy,nonn,tabl
%O A157402 1,3
%A A157402 _Peter Luschny_, Mar 09 2009, Mar 14 2009