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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.
3

%I #14 Apr 13 2017 16:49:17

%S 0,0,0,1,2,8,28,100,358,1309,4772,17556,64782,240090,892662,3329942,

%T 12456782,46725350,175698056,662193908,2501118956,9465771967,

%U 35891640172,136331485336,518702002350,1976588406300,7543137149256,28826327724850,110304963059048

%N 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.

%H Alois P. Heinz, <a href="/A056711/b056711.txt">Table of n, a(n) for n = 0..1000</a>

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

%F 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

%Y Cf. A000108, A058855, A046342.

%Y Column k=3 of A275431.

%K nonn

%O 0,5

%A _N. J. A. Sloane_, Jan 19 2001