A157395 A partition product of Stirling_1 type [parameter k = 5] with biggest-part statistic (triangle read by rows).

1, 1, 5, 1, 15, 20, 1, 105, 80, 60, 1, 425, 1200, 300, 120, 1, 3075, 10400, 5400, 720, 120, 1, 15855, 102200, 75600, 15120, 840, 0, 1, 123515, 1149120, 907200, 241920, 20160, 0, 0, 1, 757755, 12783680, 13426560, 3719520, 362880

Offset

1,3

Comments

Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = 5,

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

Underlying partition triangle is A144879.

Same partition product with length statistic is A049411.

Diagonal a(A000217(n)) = falling_factorial(5,n-1), row in A008279

Row sum is A049428.

Links

Table of n, a(n) for n=1..42.

Peter Luschny, Counting with Partitions.

Peter Luschny, Generalized Stirling_1 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-2}(j-n+7).

Crossrefs

Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395

Sequence in context: A213590 A185263 A264616 * A157385 A157397 A157405

Adjacent sequences: A157392 A157393 A157394 * A157396 A157397 A157398

Keyword

easy,nonn,tabl

Author

Peter Luschny, Mar 07 2009, Mar 14 2009

Status

approved