cp's OEIS Frontend

A157401 A partition product of Stirling_2 type [parameter k = 1] with biggest-part statistic (triangle read by rows).

%I A157401 #2 Mar 30 2012 17:27:11
%S A157401 1,1,1,1,1,3,3,1,9,12,15,1,25,60,75,105,1,75,330,450,630,945,1,231,
%T A157401 1680,3675,4410,6615,10395,1,763,9408,30975,41160,52920,83160,135135,
%U A157401 1,2619,56952,233415,489510,555660,748440,1216215
%N A157401 A partition product of Stirling_2 type [parameter k = 1] with biggest-part statistic (triangle read by rows).
%C A157401 Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 1,
%C A157401 summed over parts with equal biggest part (see the Luschny link).
%C A157401 Underlying partition triangle is A143171.
%C A157401 Same partition product with length statistic is A001497.
%C A157401 Diagonal a(A000217) = A001147.
%C A157401 Row sum is A001515.
%H A157401 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%H A157401 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling2partitions.html"> Generalized Stirling_2 Triangles</a>.
%F A157401 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157401 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157401 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157401 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(2*j - 1).
%Y A157401 Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157402, A157403, A157404, A157405
%K A157401 easy,nonn,tabl
%O A157401 1,6
%A A157401 _Peter Luschny_, Mar 09 2009, Mar 14 2009