A370570 Number of permutations of [n] having no adjacent 2-cycles and no adjacent 3-cycles.

1, 1, 1, 3, 17, 95, 594, 4280, 35018, 320636, 3249951, 36140133, 437572800, 5731086422, 80745062993, 1217782176949, 19576722067015, 334183547442139, 6037316140379389, 115082343658784617, 2308352556410956084, 48602560660569621128, 1071794851776260190000

Offset: 0

Author

Seiichi Manyama, Feb 22 2024

Keywords

• nonn

Crossrefs

Cf. A370569.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k/(1+x^2+x^3)^(k+1)))

Formula

G.f.: Sum_{k>=0} k! * x^k / (1+x^2+x^3)^(k+1).

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