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

 

Logo

The submissions stack has been unacceptably high for several months now. Please voluntarily restrict your submissions and please help with the editing. (We don't want to have to impose further limits.)

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A097763 Number of different partitions of the set {1, 2, ..., n} into an even number of blocks such that each block contains at least 2 elements. 2
0, 0, 0, 3, 10, 25, 56, 224, 1506, 9951, 57992, 315425, 1761552, 11022180, 78474748, 603715831, 4771273414, 38070877273, 309146434240, 2598546954268, 22887194502518, 211388690471531, 2031261113410564, 20121026325645745 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A097762(n)+A097763(n) = A000296(n).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..500

FORMULA

Exponential generating function: cosh(exp(x)-x-1).

EXAMPLE

a(6)=25 since we can partition a set of six elements into two non-singleton blocks, either of sizes four and two (15 ways) or three and three (10 ways); a(6)=15+10=25.

MAPLE

seq(coeff(series(cosh(exp(x)-x-1), x=0, 25), x^i)*i!, i=1..24);

# second Maple program:

with(combinat):

b:= proc(n, i, t) option remember; `if`(n=0, t,

      `if`(i<2, 0, add(multinomial(n, n-i*j, i$j)/j!*

       b(n-i*j, i-1, irem(t+j, 2)), j=0..n/i)))

    end:

a:= n-> b(n$2, 1):

seq(a(n), n=1..30);  # Alois P. Heinz, Mar 08 2015

CROSSREFS

Cf. A000296, A097762.

Sequence in context: A047667 A192963 A000247 * A034506 A067988 A005674

Adjacent sequences:  A097760 A097761 A097762 * A097764 A097765 A097766

KEYWORD

easy,nonn

AUTHOR

Isabel C. Lugo (izzycat(AT)gmail.com), Aug 23 2004

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified August 28 20:16 EDT 2015. Contains 261164 sequences.