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A212581
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Number of equivalence classes of S_n under transformations of positionally and numerically adjacent elements of the form abc <--> acb <--> bac where a<b<c.
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4
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1, 1, 2, 4, 17, 89, 556, 4011, 32843, 301210, 3059625, 34104275, 413919214, 5434093341, 76734218273, 1159776006262, 18681894258591, 319512224705645, 5782488507020050, 110407313135273127, 2218005876646727423, 46767874983437110354, 1032732727339665789981
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} k! * ( x * (1-x^2)^2/(1-x^3) )^k. - Seiichi Manyama, Feb 20 2024
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EXAMPLE
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a(3) = 4: {123, 132, 213}, {231}, {312}, {321}.
a(4) = 17: {1234, 1243, 1324, 2134}, {1342}, {1423}, {1432}, {2143}, {2314}, {2341, 2431, 3241}, {2413}, {3124}, {3142}, {3214}, {3412}, {3421}, {4123, 4132, 4213}, {4231}, {4312}, {4321}. (End)
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1-x^2)^2/(1-x^3))^k)) \\ Seiichi Manyama, Feb 20 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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