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A157403 A partition product of Stirling_2 type [parameter k = 3] with biggest-part statistic (triangle read by rows). 10
1, 1, 3, 1, 9, 21, 1, 45, 84, 231, 1, 165, 840, 1155, 3465, 1, 855, 8610, 13860, 20790, 65835, 1, 3843, 64680, 250635, 291060, 460845, 1514205, 1, 21819, 689136, 3969735, 6015240, 7373520, 12113640, 40883535, 1, 114075 (list; table; graph; refs; listen; history; text; internal format)
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 A143173.

Same partition product with length statistic is A000369.

Diagonal a(A000217) = A008545

Row sum is A016036.

LINKS

Table of n, a(n) for n=1..38.

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, A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157404, A157405

Sequence in context: A118793 A247231 A160568 * A225118 A273464 A105951

Adjacent sequences:  A157400 A157401 A157402 * A157404 A157405 A157406

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Luschny, Mar 09 2009

STATUS

approved

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Last modified September 22 09:45 EDT 2017. Contains 292337 sequences.