A303871 Number of noncrossing partitions up to rotation and reflection composed of n blocks of size 5.

1, 1, 1, 3, 11, 60, 423, 3381, 29335, 266703, 2507232, 24177705, 238003111, 2383370158, 24217426745, 249182213284, 2592138293117, 27225668134063, 288405507217589, 3078471666603235, 33085393411436772, 357782389095170193, 3890765813426578535, 42527471172438573757

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Formula

a(n) ~ 5^(5*n - 1/2) / (sqrt(Pi) * n^(5/2) * 2^(8*n + 9/2)). - Vaclav Kotesovec, Jun 01 2022

Mathematica

u[n_, k_, r_] := (r*Binomial[k*n + r, n]/(k*n + r));
e[n_, k_] := Sum[ u[j, k, 1 + (n - 2*j)*k/2], {j, 0, n/2}]
c[n_, k_] := If[n == 0, 1, (DivisorSum[n, EulerPhi[n/#]*Binomial[k*#, #] &] + DivisorSum[GCD[n - 1, k], EulerPhi[#]*Binomial[n*k/#, (n - 1)/#] &])/(k*n) - Binomial[k*n, n]/(n*(k - 1) + 1)];
T[n_, k_] := (1/2)*(c[n, k] + If[n == 0, 1, If[OddQ[k], If[OddQ[n], 2*u[Quotient[n, 2], k, (k + 1)/2], u[n/2, k, 1] + u[n/2 - 1, k, k]], e[n, k] + If[OddQ[n], u[Quotient[n, 2], k, k/2]]]/2]) /. Null -> 0;
a[n_] := T[n, 5];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 14 2018, after Andrew Howroyd and A303929 *)

Crossrefs

Column k=5 of A303929.

Cf. A054365.

Sequence in context: A075201 A362911 A136440 * A231344 A007146 A076475

Adjacent sequences: A303868 A303869 A303870 * A303872 A303873 A303874

Keyword

nonn

Author

Andrew Howroyd, May 01 2018

Status

approved