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A370324 Number of derangements of [n] having no adjacent 2-cycles, no adjacent 3-cycles, no adjacent 4-cycles and no adjacent 5-cycles. 3
1, 0, 0, 1, 6, 34, 217, 1567, 12842, 117704, 1193802, 13280778, 160843345, 2107036346, 29689965966, 447822830067, 7199604972876, 122907451783308, 2220526880775841, 42328779624824103, 849065324387063412, 17877539166289948864, 394246737752465047380 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
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
Sequence in context: A063090 A184185 A216317 * A230331 A267242 A197436
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 22 2024
STATUS
approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)