A157383 A partition product of Stirling_1 type [parameter k = -3] with biggest-part statistic (triangle read by rows).

1, 1, 3, 1, 9, 12, 1, 45, 48, 60, 1, 165, 480, 300, 360, 1, 855, 3840, 3600, 2160, 2520, 1, 3843, 29400, 46200, 30240, 17640, 20160, 1, 21819, 272832, 520800, 443520, 282240, 161280, 181440

Offset

1,3

Comments

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

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

Underlying partition triangle is A144353.

Same partition product with length statistic is A046089.

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

Row sum is A049376.

Links

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

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-1).

Crossrefs

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

Sequence in context: A354622 A173020 A334062 * A232598 A174510 A141237

Adjacent sequences: A157380 A157381 A157382 * A157384 A157385 A157386

Keyword

easy,nonn,tabl

Author

Peter Luschny, Mar 07 2009, Mar 14 2009

Status

approved