A157399 - OEIS

A157399

A partition product of Stirling_2 type [parameter k = -3] with biggest-part statistic (triangle read by rows).

1, 1, 3, 1, 9, 15, 1, 45, 60, 105, 1, 165, 600, 525, 945, 1, 855, 5250, 6300, 5670, 10395, 1, 3843, 39900, 91875, 79380, 72765, 135135, 1, 21819, 391440, 1164975, 1323000, 1164240, 1081080, 2027025, 1

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OFFSET

1,3

COMMENTS

Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = -3,

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

Underlying partition triangle is A134144.

Same partition product with length statistic is A035342.

Diagonal a(A000217) = A001147.

Row sum is A049118.

LINKS

Table of n, a(n) for n=1..37.

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}(-2*j - 1).

CROSSREFS

Cf. A157396, A157397, A157398, A157400, A080510, A157401, A157402, A157403, A157404, A157405

Sequence in context: A174510 A141237 A318391 * A288852 A162749 A094796

Adjacent sequences: A157396 A157397 A157398 * A157400 A157401 A157402

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Luschny, Mar 09 2009, Mar 14 2009

STATUS

approved