A056711 Plug g.f. for A000108 (minus the leading 1), 1/2*(1-(1-4*x)^(1/2))/x - 1, into cycle index for dihedral group D_3.

0, 0, 0, 1, 2, 8, 28, 100, 358, 1309, 4772, 17556, 64782, 240090, 892662, 3329942, 12456782, 46725350, 175698056, 662193908, 2501118956, 9465771967, 35891640172, 136331485336, 518702002350, 1976588406300, 7543137149256, 28826327724850, 110304963059048

Offset: 0

Author

N. J. A. Sloane, Jan 19 2001

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000108, A058855, A046342.

Column k=3 of A275431.

Formula

Cycle index for D_3: 1/6*Z[1]^3+1/2*Z[1]*Z[2]+1/3*Z[3].

O.g.f.: 1/6*A(x)^3 + 1/2*A(x)*A(x^2) + 1/3*A(x^3), with A(x):=1/2*(1-(1-4*x)^(1/2))/x - 1 (see the name). For the cycle index of the dihedral group D_n see A212355 for the Harary-Palmer reference, the formula and a link. - Wolfdieter Lang, Jun 02 2012