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 A129535 Number of permutations of 1,...,n with at least one pair of adjacent consecutive entries (i.e., of the form k(k+1) or (k+1)k), n >= 2. 3
 2, 6, 22, 106, 630, 4394, 35078, 315258, 3149494, 34620010, 415222566, 5395737242, 75516784982, 1132471183626, 18115911832390, 307919970965434, 5541804787940598, 105282261866132138, 2105441434230129254, 44210612765653749210, 972564180363044943766 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Column 1 of A129534. a(n) = n! - A002464(n). Column k=2 of A322481. REFERENCES R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 6.40. LINKS Alois P. Heinz, Table of n, a(n) for n = 2..450 FORMULA G.f.: E(x) - E(x(1-x)/(1+x)), where E(x) = Sum_{n>=0} n!*x^n. a(n) = n! - Sum_{k=1..n} ((-1)^(n-k)*k!*Sum_{i=0..n-k} binomial(i+k-1, k-1)*binomial(k, n-i-k)), n > 0. - Vladimir Kruchinin, Sep 08 2010 EXAMPLE a(4)=22 because 3142 and 2413 are the only permutations of 1,2,3,4 with no adjacent consecutive entries. MAPLE E:=x->sum(n!*x^n, n=0..35): G:=E(x)-E(x*(1-x)/(1+x)): Gser:=series(G, x=0, 30): seq(coeff(Gser, x, n), n=2..23); CROSSREFS Cf. A002464, A129534, A322481. Sequence in context: A103941 A064643 A218531 * A216720 A290279 A014371 Adjacent sequences:  A129532 A129533 A129534 * A129536 A129537 A129538 KEYWORD nonn AUTHOR Emeric Deutsch, May 05 2007 STATUS approved

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Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)