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A370569
Number of permutations of [n] having no adjacent 2-cycles and no adjacent 4-cycles.
3
1, 1, 1, 4, 18, 97, 607, 4358, 35523, 324356, 3280902, 36427352, 440515699, 5764104507, 81147821501, 1223090709078, 19651920713844, 335323035157947, 6055709997021397, 115397482250691724, 2314064310772997407, 48711753977589111112, 1073990818947724506060
OFFSET
0,4
FORMULA
G.f.: Sum_{k>=0} k! * x^k * ( (1-x^2)/(1-x^6) )^(k+1).
a(n) = Sum_{i, j>=0 and 2*i+4*j<=n} (-1)^(i+j) * (n-i-3*j)!/(i!*j!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k*((1-x^2)/(1-x^6))^(k+1)))
CROSSREFS
Sequence in context: A334735 A086681 A054139 * A020072 A020027 A263688
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 22 2024
STATUS
approved