A157393 A partition product of Stirling_1 type [parameter k = 3] with biggest-part statistic (triangle read by rows).

1, 1, 3, 1, 9, 6, 1, 45, 24, 6, 1, 165, 240, 30, 0, 1, 855, 1560, 360, 0, 0, 1, 3843, 12180, 3360, 0, 0, 0, 1, 21819, 96096, 30660, 0, 0, 0, 0, 1, 114075, 794304, 318276, 0, 0, 0, 0, 0, 1, 703215, 6850080, 3270960, 0, 0, 0, 0, 0, 0, 1, 4125495, 62516520, 35053920, 0, 0

Offset

1,3

Comments

Partition product 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 A144877.

Same partition product with length statistic is A049410.

Diagonal a(A000217(n)) = falling_factorial(3,n-1), row in A008279.

Row sum is A049426.

Links

Table of n, a(n) for n=1..61.

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+5).

Crossrefs

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

Sequence in context: A236420 A187537 A246256 * A242402 A217629 A127552

Adjacent sequences: A157390 A157391 A157392 * A157394 A157395 A157396

Keyword

easy,nonn,tabl

Author

Peter Luschny, Mar 07 2009, Mar 14 2009

Status

approved