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A157386 A partition product of Stirling_1 type [parameter k = -6] with biggest-part statistic (triangle read by rows). 10
1, 1, 6, 1, 18, 42, 1, 144, 168, 336, 1, 600, 2940, 1680, 3024, 1, 4950, 33600, 35280, 18144, 30240, 1, 26586, 336630, 717360, 444528, 211680, 332640, 1, 234528, 4870992, 11313120, 10329984, 5927040, 2661120, 3991680 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = -6,

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

Underlying partition triangle is A144356.

Same partition product with length statistic is A049374.

Diagonal a(A000217(n)) = rising_factorial(6,n-1), A001725(n+4).

Row sum is A049402.

LINKS

Table of n, a(n) for n=1..36.

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-4).

CROSSREFS

Cf. A157385, A157384, A157383, A157400, A126074, A157391, A157392, A157393, A157394, A157395

Sequence in context: A277068 A092371 A187552 * A157396 A019430 A064083

Adjacent sequences:  A157383 A157384 A157385 * A157387 A157388 A157389

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Luschny, Mar 07 2009, Mar 14 2009

STATUS

approved

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Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.