A192894 Number of symmetric 13-ary factorizations of the n-cycle (1,2...n).

1, 1, 1, 7, 13, 112, 247, 2310, 5525, 53998, 135408, 1360289, 3518515, 36017352, 95223414, 988172368, 2655417765, 27844071255, 75769712590, 801012669457, 2201663313200, 23428926096576, 64924369564353, 694644371065372, 1938034271677595, 20829931845958872, 58448142042957576

Offset

0,4

Comments

The six sequences displayed in Table 1 of the Bousquet-Lamathe reference are A047749, A143546, A143547, A143554, A192893, A192894. From this one should be able to guess a g.f.

Links

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

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 Seiichi Manyama, Jul 07 2025: (Start)

G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x)*A(-x))^6 ).

G.f. A(x) satisfies A(x)*A(-x) = (A(x) + A(-x))/2 = G(x^2), where G(x) = 1 + x*G(x)^13.

a(0) = 1; a(n) = Sum_{x_1, x_2, ..., x_7>=0 and x_1+2*(x_2+x_3+...+x_7)=n-1} a(x_1) * Product_{k=2..7} a(2*x_k). (End)

a(0) = 1; a(n) = Sum_{x_1, x_2, ..., x_13>=0 and x_1+x_2+...+x_13=n-1} (-1)^(x_1+x_2+x_3+x_4+x_5+x_6) * Product_{k=1..13} a(x_k). - Seiichi Manyama, Jul 09 2025

Crossrefs

Column k=13 of A369929 and k=14 of A370062.

Cf. A143049.

Sequence in context: A046519 A283920 A128351 * A367597 A241280 A219703

Adjacent sequences: A192891 A192892 A192893 * A192895 A192896 A192897

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 Seiichi Manyama, Jul 07 2025

Status

approved