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A295198 Number of noncrossing partitions up to rotation of an n-set without singleton blocks. 4
1, 0, 1, 1, 2, 2, 5, 6, 15, 28, 67, 145, 368, 870, 2211, 5549, 14290, 36824, 96347, 252927, 670142, 1783770, 4777951, 12855392, 34756783, 94345664, 257114389, 703150507, 1929404736, 5310364234, 14658134277, 40569137070, 112566363319, 313074271844, 872677323283 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

a(n) = (1/n) * (A005043(n) - A002426(n) + Sum_{d|n} phi(n/d) * A002426(d)).

MATHEMATICA

b[0] = 1; b[1] = 0; b[n_] := b[n] = (n-1)*(2*b[n-1] + 3*b[n-2])/(n+1);

a[0] = 1; a[n_] := (b[n] + Sum[EulerPhi[n/d]*Coefficient[(1 + x + x^2)^d, x, d], {d, Most @ Divisors[n]}])/n;

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Jul 03 2018, after Andrew Howroyd *)

PROG

(PARI)  \\ here b(n) is A005043.

b(n) = {polcoeff(serreverse((x - x^3) / (1 + x^3) + x * O(x*x^n)), n+1)}

a(n) = {if(n<1, n==0, (b(n) + sumdiv(n, d, if(d<n, eulerphi(n/d) * polcoeff((1 + x + x^2)^d, d))))/n)}

CROSSREFS

Column k=0 of A211357.

Cf. A005043 (noncrossing partitions of an n-set without singleton blocks).

Cf. A002426.

Sequence in context: A345470 A320296 A329908 * A080880 A305606 A120843

Adjacent sequences:  A295195 A295196 A295197 * A295199 A295200 A295201

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Nov 16 2017

STATUS

approved

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Last modified August 3 01:36 EDT 2021. Contains 346429 sequences. (Running on oeis4.)