login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A157383 A partition product of Stirling_1 type [parameter k = -3] with biggest-part statistic (triangle read by rows). 10
1, 1, 3, 1, 9, 12, 1, 45, 48, 60, 1, 165, 480, 300, 360, 1, 855, 3840, 3600, 2160, 2520, 1, 3843, 29400, 46200, 30240, 17640, 20160, 1, 21819, 272832, 520800, 443520, 282240, 161280, 181440 (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 = -3,

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

Underlying partition triangle is A144353.

Same partition product with length statistic is A046089.

Diagonal a(A000217(n)) = rising_factorial(3,n-1), A001710(n+1).

Row sum is A049376.

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-1).

CROSSREFS

Cf. A157386, A157385, A157384, A157400, A126074, A157391, A157392, A157393, A157394, A157395

Sequence in context: A260285 A242499 A173020 * A232598 A174510 A141237

Adjacent sequences:  A157380 A157381 A157382 * A157384 A157385 A157386

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Luschny, Mar 07 2009, Mar 14 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

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