A157383 - OEIS

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

%S 1,1,3,1,9,12,1,45,48,60,1,165,480,300,360,1,855,3840,3600,2160,2520,

%T 1,3843,29400,46200,30240,17640,20160,1,21819,272832,520800,443520,

%U 282240,161280,181440

%N A partition product of Stirling_1 type [parameter k = -3] with biggest-part statistic (triangle read by rows).

%C Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = -3,

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

%C Underlying partition triangle is A144353.

%C Same partition product with length statistic is A046089.

%C Diagonal a(A000217(n)) = rising_factorial(3,n-1), A001710(n+1).

%C Row sum is A049376.

%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/stirling1partitions.html"> Generalized Stirling_1 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-2}(j-n-1).

%Y Cf. A157386, A157385, A157384, A157400, A126074, A157391, A157392, A157393, A157394, A157395

%K easy,nonn,tabl

%O 1,3

%A _Peter Luschny_, Mar 07 2009, Mar 14 2009