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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

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

a(n) = A000296(n) - A097762(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

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i < 2, 0, Sum[multinomial[n, Join[{n - i*j}, Array[i &, j]]]/j!*b[n - i*j, i - 1, Mod[t + j, 2]], {j, 0, n/i}]]]; a[n_] := b[n, n, 1];  Table[a[n], {n, 1, 30}] (* Jean-Fran├žois Alcover, Jan 10 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A000296, A097762.

Sequence in context: A047667 A192963 A000247 * A034506 A067988 A297186

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 | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)