A370569 Number of permutations of [n] having no adjacent 2-cycles and no adjacent 4-cycles.

1, 1, 1, 4, 18, 97, 607, 4358, 35523, 324356, 3280902, 36427352, 440515699, 5764104507, 81147821501, 1223090709078, 19651920713844, 335323035157947, 6055709997021397, 115397482250691724, 2314064310772997407, 48711753977589111112, 1073990818947724506060

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

G.f.: Sum_{k>=0} k! * x^k * ( (1-x^2)/(1-x^6) )^(k+1).

a(n) = Sum_{i, j>=0 and 2*i+4*j<=n} (-1)^(i+j) * (n-i-3*j)!/(i!*j!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k*((1-x^2)/(1-x^6))^(k+1)))

Crossrefs

Cf. A177251, A370324.

Sequence in context: A334735 A086681 A054139 * A020072 A020027 A263688

Adjacent sequences: A370566 A370567 A370568 * A370570 A370571 A370572

Keyword

nonn

Author

Seiichi Manyama, Feb 22 2024

Status

approved