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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A144151 Triangle T(n,k), n>=0, 0<=k<=n, read by rows: T(n,k) = number of ways an undirected cycle of length k can be built from n labeled nodes. 10
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 3, 1, 5, 10, 10, 15, 12, 1, 6, 15, 20, 45, 72, 60, 1, 7, 21, 35, 105, 252, 420, 360, 1, 8, 28, 56, 210, 672, 1680, 2880, 2520, 1, 9, 36, 84, 378, 1512, 5040, 12960, 22680, 20160, 1, 10, 45, 120, 630, 3024, 12600, 43200, 113400, 201600, 181440 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA T(n,k) = C(n,k) if k<=2, else T(n,k) = C(n,k)*(k-1)!/2. E.g.f.: exp(x)*(log(1/(1 - y*x))/2 + 1 + y*x/2 + (y*x)^2/4). - Geoffrey Critzer, Jul 22 2016 EXAMPLE T(4,3) = 4, because 4 undirected cycles of length 3 can be built from 4 labeled nodes: .1.2. .1.2. .1-2. .1-2. ../|. .|\.. ..\|. .|/.. .3-4. .3-4. .3.4. .3.4. Triangle begins: 1; 1, 1; 1, 2, 1; 1, 3, 3, 1; 1, 4, 6, 4, 3; 1, 5, 10, 10, 15, 12; ... MAPLE T:= (n, k)-> if k<=2 then binomial(n, k) else mul(n-j, j=0..k-1)/k/2 fi: seq(seq(T(n, k), k=0..n), n=0..12); MATHEMATICA t[n_, k_ /; k <= 2] := Binomial[n, k]; t[n_, k_] := Binomial[n, k]*(k-1)!/2; Table[t[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 18 2013 *) CoefficientList[Table[1 + n x (2 + (n - 1) x + 2 HypergeometricPFQ[{1, 1, 1 - n}, {2}, -x])/4, {n, 0, 10}], x] (* Eric W. Weisstein, Apr 06 2017 *) CROSSREFS Columns 0-4 give: A000012, A000027, A000217, A000292, A050534. Diagonal gives: A001710. Cf. A000142, A007318. Row sums are in A116723. - Alois P. Heinz, Jun 01 2009 Excluding columns k=0,1,and 2 the row sums are A002807. - Geoffrey Critzer, Jul 22 2016 Cf. A284947 (k-cycle counts for k >= 3 in the complete graph K_n). - Eric W. Weisstein, Apr 06 2017 T(2n,n) gives A006963(n+1) for n>=3. Sequence in context: A026022 A073714 A171848 * A022818 A050447 A248601 Adjacent sequences: A144148 A144149 A144150 * A144152 A144153 A144154 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Sep 12 2008 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.

Last modified September 21 11:35 EDT 2023. Contains 365501 sequences. (Running on oeis4.)