_Peter Luschny (peter(AT)luschny.de), _, Mar 09 2009, Mar 14 2009

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

1, 1, 1, 1, 1, 3, 3, 1, 9, 12, 15, 1, 25, 60, 75, 105, 1, 75, 330, 450, 630, 945, 1, 231, 1680, 3675, 4410, 6615, 10395, 1, 763, 9408, 30975, 41160, 52920, 83160, 135135, 1, 2619, 56952, 233415, 489510, 555660, 748440, 1216215

1,6

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

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

Underlying partition triangle is A143171.

Same partition product with length statistic is A001497.

Diagonal a(A000217) = A001147.

Row sum is A001515.

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

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

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

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

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

f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-1}(2*j - 1).

Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157402, A157403, A157404, A157405

easy,nonn,tabl

Peter Luschny (peter(AT)luschny.de), Mar 09 2009, Mar 14 2009

approved