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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A168605 Number of ways of partitioning the multiset {1,1,1,2,3,...,n-2} into exactly three nonempty parts. 3
1, 2, 8, 30, 104, 342, 1088, 3390, 10424, 31782, 96368, 291150, 877544, 2640822, 7938848, 23849310, 71613464, 214971462, 645176528, 1936053870, 5809210184, 17429727702, 52293377408, 156888520830, 470682339704, 1412080573542 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Table of n, a(n) for n=3..28.

M. Griffiths, I. Mezo, A generalization of Stirling Numbers of the Second Kind via a special multiset, JIS 13 (2010) #10.2.5

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

FORMULA

a(3)=1 and, for n>=4, a(n)=(5*3^(n-3)-3*2^(n-2)+3)/3.

The shifted e.g.f. is (5e^(3x)-6e^(2x)+3e^x+1)/3.

G.f.: x^3(1-4x+7x^2-2x^3)/((1-x)(1-2x)(1-3x)).

MATHEMATICA

f5[n_] := (5 3^(n - 3) - 3 2^(n - 2) + 3)/3; Table[f5[n], {n, 4, 28}]

CROSSREFS

The number of ways of partitioning the multiset {1, 1, 1, 2, 3, ..., n-1} into exactly two and four nonempty parts are given in A168604 and A168606, respectively.

Sequence in context: A010749 A299415 A230701 * A127865 A199923 A230269

Adjacent sequences:  A168602 A168603 A168604 * A168606 A168607 A168608

KEYWORD

nonn,easy

AUTHOR

Martin Griffiths, Dec 01 2009

EXTENSIONS

Last element of the multiset in the definition corrected by Martin Griffiths, Dec 02 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 20 06:26 EST 2019. Contains 320332 sequences. (Running on oeis4.)