A157396 A partition product of Stirling_2 type [parameter k = -6] with biggest-part statistic (triangle read by rows).

1, 1, 6, 1, 18, 66, 1, 144, 264, 1056, 1, 600, 4620, 5280, 22176, 1, 4950, 68640, 110880, 133056, 576576, 1, 26586, 639870, 3141600, 3259872, 4036032, 17873856, 1, 234528, 10759056, 69263040, 105557760, 113008896, 142990848

Offset

1,3

Comments

Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = -6,

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

Underlying partition triangle is A134278.

Same partition product with length statistic is A049385.

Diagonal a(A000217) = A008548.

Row sum is A049412.

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}(-5*j - 1).

Crossrefs

Cf. A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405

Sequence in context: A092371 A187552 A157386 * A019430 A064083 A152249

Adjacent sequences: A157393 A157394 A157395 * A157397 A157398 A157399

Keyword

easy,nonn,tabl

Author

Peter Luschny, Mar 09 2009

Extensions

Offset corrected by Peter Luschny, Mar 14 2009

Status

approved