A157397 A partition product of Stirling_2 type [parameter k = -5] with biggest-part statistic (triangle read by rows).

1, 1, 5, 1, 15, 45, 1, 105, 180, 585, 1, 425, 2700, 2925, 9945, 1, 3075, 34650, 52650, 59670, 208845, 1, 15855, 308700, 1248975, 1253070, 1461915, 5221125, 1, 123515, 4475520, 23689575, 33972120, 35085960, 41769000

Offset

1,3

Comments

Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = -5,

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

Underlying partition triangle is A134273.

Same partition product with length statistic is A049029.

Diagonal a(A000217) = A007696.

Row sum is A049120.

Links

Table of n, a(n) for n=1..35.

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}(-4*j - 1).

Crossrefs

Cf. A157396, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405

Sequence in context: A264616 A157395 A157385 * A157405 A283434 A019429

Adjacent sequences: A157394 A157395 A157396 * A157398 A157399 A157400

Keyword

easy,nonn,tabl

Author

Peter Luschny, Mar 09 2009

Extensions

Offset corrected by Peter Luschny, Mar 14 2009

Status

approved