A157404 A partition product of Stirling_2 type [parameter k = 4] with biggest-part statistic (triangle read by rows).

1, 1, 4, 1, 12, 36, 1, 72, 144, 504, 1, 280, 1800, 2520, 9576, 1, 1740, 22320, 37800, 57456, 229824, 1, 8484, 182700, 864360, 1005480, 1608768, 6664896, 1, 57232, 2380896, 16546320, 26276544, 32175360, 53319168, 226606464

Offset

1,3

Comments

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

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

Underlying partition triangle is A144267.

Same partition product with length statistic is A011801.

Diagonal a(A000217) = A008546.

Row sum is A028575.

Links

Table of n, a(n) for n=1..36.

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}(5*j - 1).

Crossrefs

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

Sequence in context: A019237 A019238 A299523 * A135704 A373394 A002564

Adjacent sequences: A157401 A157402 A157403 * A157405 A157406 A157407

Keyword

easy,nonn,tabl

Author

Peter Luschny, Mar 09 2009

Status

approved