A036723 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).

1, 1, 2, 8, 30, 135, 622, 3032, 15134, 77506, 403780, 2135588, 11430910, 61815916, 337193808, 1853183376, 10251612034, 57037706410, 318965425380, 1791842232154, 10107161112356, 57221612791015, 325045726349906, 1852055247196164, 10582212069299974, 60619677502607406

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)^4 + A(x^2)^2)/2. - Andrew Howroyd, Jul 23 2026

Prog

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

Crossrefs

Column k=2 of A398106.

Cf. A036717-A036722.

Sequence in context: A150783 A150784 A150785 * A150786 A150787 A150788

Adjacent sequences: A036720 A036721 A036722 * A036724 A036725 A036726

Keyword

nonn,changed

Author

N. J. A. Sloane

Status

approved