%I #2 Mar 30 2012 17:27:11

%S 1,1,4,1,12,36,1,72,144,504,1,280,1800,2520,9576,1,1740,22320,37800,

%T 57456,229824,1,8484,182700,864360,1005480,1608768,6664896,1,57232,

%U 2380896,16546320,26276544,32175360,53319168,226606464

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

%C Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 4,

%C summed over parts with equal biggest part (see the Luschny link).

%C Underlying partition triangle is A144267.

%C Same partition product with length statistic is A011801.

%C Diagonal a(A000217) = A008546.

%C Row sum is A028575.

%H Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.

%H Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.

%F T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n

%F T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that

%F 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),

%F f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(5*j - 1).

%Y Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157405

%K easy,nonn,tabl

%O 1,3

%A _Peter Luschny_, Mar 09 2009