A036725 G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 2 generated by (1,2)(3,4)(5,6)(7,8).

1, 1, 4, 32, 268, 2574, 26004, 274752, 2990412, 33321801, 378155340, 4355839608, 50792907100, 598432565856, 7112882558060, 85186232560504, 1026982086302284, 12453151958594288, 151785836438975264, 1858565360218893144, 22851521570687098564, 282012877022531411468, 3492121681361229899816

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Formula

G.f. A(x) satisfies A(x) = 1 + x*(A(x)^8 + A(x^2)^4)/2. - Andrew Howroyd, Jul 23 2026

Prog

(PARI) seq(n) = {my(g=O(1)); for(i=0, n, g = 1+x*(g^8 + subst(g^4, x, x^2))/2); Vec(g)} \\ Andrew Howroyd, Jul 23 2026

Crossrefs

Column k=4 of A398106.

Cf. A036717-A036724.

Sequence in context: A092811 A363440 A009509 * A065089 A113329 A246818

Adjacent sequences: A036722 A036723 A036724 * A036726 A036727 A036728

Keyword

nonn,changed

Author

N. J. A. Sloane

Status

approved