A370323 Number of derangements of [n] having no adjacent 2-cycles, no adjacent 3-cycles and no adjacent 4-cycles.

1, 0, 0, 1, 6, 35, 217, 1568, 12848, 117738, 1194019, 13282346, 160856190, 2107154067, 29691159876, 447836111629, 7199765822643, 122909558878512, 2220556571338744, 42329227454294820, 849072524072460101, 17877662074795269964, 394248958294191005180

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^5) )^(k+1).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k*((1-x)/(1-x^5))^(k+1)))

Crossrefs

Cf. A000166, A177258, A177261, A370324.

Sequence in context: A291246 A117671 A354136 * A317409 A354324 A213452

Adjacent sequences: A370320 A370321 A370322 * A370324 A370325 A370326

Keyword

nonn

Author

Seiichi Manyama, Feb 22 2024

Status

approved