login
A192893
Number of symmetric 11-ary factorizations of the n-cycle (1,2...n).
4
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
0,4
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
Michel Bousquet and Cédric Lamathe, On symmetric structures of order two, Discrete Math. Theor. Comput. Sci. 10 (2008), 153-176. See Table 1.
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. satisfies: A(x) = 1 + x*A(x)^6*A(-x)^5. (End)
PROG
(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
CROSSREFS
Column k=11 of A369929 and k=12 of A370062.
Sequence in context: A332659 A219702 A013321 * A188599 A217934 A012419
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 12 2011
EXTENSIONS
a(11) onwards from Andrew Howroyd, Jan 26 2024
a(0)=1 prepended by Andrew Howroyd, Feb 08 2024
STATUS
approved