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 A129118 For each permutation p of {1,2,...,n} define minabsjump(p) = min(|p(i) - i|, 1<=i<=n); a(n) is the sum of minabsjumps of all p. 1
 0, 1, 2, 10, 48, 295, 2068, 16654, 150382, 1508500, 16631696, 199966907, 2603709640, 36501212971, 548150650582, 8779185528284, 149376644391508, 2690852138104504, 51161190374132154, 1023850096381041159, 21512688329462044264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA a(n) = Sum_{k=1..floor(n/2)} k * A299789(n,k). - Alois P. Heinz, Jan 21 2019 MAPLE n:=8; with(combinat); P:=permute(n); ct:= 0; for j to factorial(n) do ct:= ct+min(seq(abs(P[j][i]-i), i=1..n)) end do: ct; # yields a(n) for the specified n - Emeric Deutsch, Aug 24 2007 # second Maple program: b:= proc(s) option remember; (n-> `if`(n=1, x^(s[]-1), add((p->       add(coeff(p, x, i)*x^min(i, abs(n-j)), i=0..degree(p)))(         b(s minus {j})), j=s)))(nops(s))     end: a:= n-> (p-> add(coeff(p, x, i)*i, i=1..n-1))(b({\$1..n})): seq(a(n), n=1..15);  # Alois P. Heinz, Jan 21 2019 PROG (C++) #include #include #include using namespace std; inline int mabsj(const vector & s) { const int n = s.size() ; int mi =n ; for(int i=0; i s; for(int i=1; i<=n; i++) s.push_back(i) ; unsigned long long resul=0 ; do { resul += mabsj(s) ; } while( next_permutation(s.begin(), s.end()) ) ; cout << n << " " << resul << endl ; } return 0 ; } - R. J. Mathar, Nov 01 2007 CROSSREFS Cf. A130153, A018927, A299789. Sequence in context: A200540 A166922 A302557 * A037256 A270664 A330543 Adjacent sequences:  A129115 A129116 A129117 * A129119 A129120 A129121 KEYWORD more,nonn AUTHOR Emeric Deutsch, Vladeta Jovovic, Jun 07 2007 EXTENSIONS One more term from Emeric Deutsch, Aug 24 2007 a(11)-a(13) from R. J. Mathar, Nov 01 2007 a(14) from Donovan Johnson, Sep 24 2010 a(15)-a(21) from Alois P. Heinz, Jan 21 2019 STATUS approved

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Last modified March 28 20:01 EDT 2020. Contains 333103 sequences. (Running on oeis4.)