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A370323
Number of derangements of [n] having no adjacent 2-cycles, no adjacent 3-cycles and no adjacent 4-cycles.
1
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 22 2024
STATUS
approved