A370324 Number of derangements of [n] having no adjacent 2-cycles, no adjacent 3-cycles, no adjacent 4-cycles and no adjacent 5-cycles.

1, 0, 0, 1, 6, 34, 217, 1567, 12842, 117704, 1193802, 13280778, 160843345, 2107036346, 29689965966, 447822830067, 7199604972876, 122907451783308, 2220526880775841, 42328779624824103, 849065324387063412, 17877539166289948864, 394246737752465047380

Offset

0,5

Links

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

Formula

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

a(n) = Sum_{i, j, k, l, m>=0 and i+2*j+3*k+4*l+5*m<=n} (-1)^(i+j+k+l+m) * (n-j-2*k-3*l-4*m)!/(i!*j!*k!*l!*m!).

Prog

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

Crossrefs

Cf. A000166, A177258, A177261, A370323.

Cf. A177251, A370569.

Sequence in context: A063090 A184185 A216317 * A230331 A267242 A197436

Adjacent sequences: A370321 A370322 A370323 * A370325 A370326 A370327

Keyword

nonn

Author

Seiichi Manyama, Feb 22 2024

Status

approved