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

1, 1, 2, 1, 6, 10, 1, 24, 40, 80, 1, 80, 300, 400, 880, 1, 330, 2400, 3600, 5280, 12320, 1, 1302, 15750, 47600, 55440, 86240, 209440, 1, 5936, 129360, 588000, 837760, 1034880, 1675520, 4188800, 1, 26784, 1146040, 5856480

Offset

1,3

Comments

Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 2,

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

Underlying partition triangle is A143172.

Same partition product with length statistic is A004747.

Diagonal a(A000217) = A008544.

Row sum is A015735.

Links

Table of n, a(n) for n=1..40.

Peter Luschny, Counting with Partitions.

Peter Luschny, Generalized Stirling_2 Triangles.

Formula

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}(3*j - 1).

Crossrefs

Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157403, A157404, A157405

Sequence in context: A348108 A177863 A193601 * A069114 A173773 A305512

Adjacent sequences: A157399 A157400 A157401 * A157403 A157404 A157405

Keyword

easy,nonn,tabl

Author

Peter Luschny, Mar 09 2009, Mar 14 2009

Status

approved