login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187250 Triangle read by rows: T(n,k) is the number of permutations of [n] having k cycles with at least 3 alternating runs (it is assumed that the smallest element of a cycle is in the first position), 0<=k<=floor(n/4). 2
1, 1, 2, 6, 22, 2, 94, 26, 460, 260, 2532, 2508, 15420, 24760, 140, 102620, 254968, 5292, 739512, 2760432, 128856, 5729192, 31547344, 2640264, 47429896, 381339368, 50186136, 46200, 417429800, 4879612808, 926494712, 3483480, 3888426512, 66107044176, 17025751600, 157068912 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of entries in row n is 1+floor(n/4).

Sum of entries in row n is n!.

T(n,0)=A187251(n).

Sum(k*T(n,k), k>=0) = A187252(n).

LINKS

Table of n, a(n) for n=0..35.

FORMULA

E.g.f.: G(t,z) = exp[(1/4)(1-t)(2z-1+exp(2z))]/(1-z)^t.

The 4-variate g.f. H(u,v,w,z) (exponential with respect z), where u marks number of cycles with 1 alternating run, v marks number of cycles with 2 alternating runs, w marks the number of all cycles, and z marks the size of the permutation, is given by H(u,v,w,z) = exp[(1/4)w((v-1)(exp(2z)+2z)+4(u-v)exp(z)+1-4u+3v)]/(1-z)^w.

We have G(t,z) = H(1/t,1/t,t,z).

EXAMPLE

T(4,1)=2 because we have (1324) and (1423).

Triangle starts:

1;

1;

2;

6;

22,2;

94,26;

460,260;

MAPLE

G := exp((1/4*(1-t))*(2*z-1+exp(2*z)))/(1-z)^t: Gser := simplify(series(G, z = 0, 17)): for n from 0 to 14 do P[n] := sort(factorial(n)*coeff(Gser, z, n)) end do: for n from 0 to 14 do seq(coeff(P[n], t, k), k = 0 .. floor((1/4)*n)) end do; # yields sequence in triangular form

CROSSREFS

Cf. A187244, A187247, A187251, A187252.

Sequence in context: A182544 A216120 A216964 * A129534 A216719 A085286

Adjacent sequences:  A187247 A187248 A187249 * A187251 A187252 A187253

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Mar 08 2011

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 1 09:18 EST 2021. Contains 349426 sequences. (Running on oeis4.)