login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A360588 Expansion of e.g.f. (exp(x)-1)^2*(x+x^2/2). 0
0, 0, 0, 6, 36, 130, 390, 1064, 2744, 6822, 16530, 39292, 92004, 212810, 487214, 1105680, 2490096, 5570254, 12385962, 27393668, 60292700, 132120114, 288357894, 627047896, 1358953896, 2936012150, 6325009730, 13589544204, 29125246164, 62277024922, 132875549790, 282930969632, 601295420384 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
a(n) is the number of ordered set partitions of an n-set into 3 sets such that the first and second sets contain at least one element and the third set contains either one or two elements.
LINKS
FORMULA
a(n) = n*2^(n-1) + binomial(n,2)*(2^(n-2)-2) - 2*n, n >= 3, a(n) = 0 otherwise.
EXAMPLE
a(5)=130 since the set partitions are the following:
20 of the form {1,2,3}, {4}, {5};
20 of the form {1}, {2,3,4}, {5};
30 of the form {1,2}, {3,4}, {5};
30 of the form {1,2}, {3}, {4,5};
30 of the form {1}, {2,3}, {4,5}.
PROG
(PARI) a(n) = if (n>=3, n*2^(n-1) + binomial(n, 2)*(2^(n-2)-2) - 2*n, 0); \\ Michel Marcus, Feb 13 2023
CROSSREFS
Sequence in context: A253945 A331576 A056375 * A321579 A364429 A018214
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Feb 12 2023
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 16:59 EDT 2024. Contains 373530 sequences. (Running on oeis4.)