A192893 Number of symmetric 11-ary factorizations of the n-cycle (1,2...n).

1, 1, 1, 6, 11, 81, 176, 1406, 3311, 27636, 68211, 585162, 1489488, 13019909, 33870540, 300138696, 793542167, 7105216833, 19022318084, 171717015470, 464333035881, 4219267597578, 11502251937176, 105085831400550, 288417894029200, 2647012241261856, 7306488667126803

Offset: 0

Author

N. J. A. Sloane, Jul 12 2011

Keywords

• nonn

Comments

The six sequences displayed in Table 1 of the Bousquet-Lamathe reference are A047749, A143546, A143547, A143554, this sequence, and A192894. From this one should be able to guess a g.f.

Number of achiral noncrossing partitions composed of n blocks of size 11. - Andrew Howroyd, Feb 08 2024

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• Michel Bousquet and Cédric Lamathe, On symmetric structures of order two, Discrete Math. Theor. Comput. Sci. 10 (2008), 153-176. See Table 1.

Crossrefs

Column k=11 of A369929 and k=12 of A370062.

Cf. A143048.

Programs

PARI

a(n)={my(m=n\2, p=5*(n%2)+1); binomial(11*m+p-1, m)*p/(10*m+p)} \\ Andrew Howroyd, Feb 08 2024

Formula

From Andrew Howroyd, Feb 08 2024: (Start)

a(2n) = binomial(11*n,n)/(10*n+1); a(2n+1) = binomial(11*n+5,n)*6/(10*n+6).

G.f. A(x) satisfies A(x) = 1 + x*A(x)^6*A(-x)^5. (End)

From Seiichi Manyama, Jul 07 2025: (Start)

G.f. A(x) satisfies A(x)*A(-x) = (A(x) + A(-x))/2 = G(x^2), where G(x) = 1 + x*G(x)^11 is the g.f. of A230388.

a(0) = 1; a(n) = Sum_{x_1, x_2, ..., x_6>=0 and x_1+2*(x_2+x_3+...+x_6)=n-1} a(x_1) * Product_{k=2..6} a(2*x_k). (End)

a(0) = 1; a(n) = Sum_{x_1, x_2, ..., x_11>=0 and x_1+x_2+...+x_11=n-1} (-1)^(x_1+x_2+x_3+x_4+x_5) * Product_{k=1..11} a(x_k). - Seiichi Manyama, Jul 09 2025

Extensions

a(11) onwards from Andrew Howroyd, Jan 26 2024

a(0)=1 prepended by Andrew Howroyd, Feb 08 2024