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 A180190 Triangle read by rows: T(n,k) is the number of permutations p of [n] for which k is the smallest among the positive differences p(i+1) - p(i); k=0 for the reversal of the identity permutation (0<=k<=n-1). 3
 1, 1, 1, 1, 3, 2, 1, 13, 6, 4, 1, 67, 30, 14, 8, 1, 411, 178, 80, 34, 16, 1, 2921, 1236, 530, 234, 86, 32, 1, 23633, 9828, 4122, 1744, 702, 226, 64, 1, 214551, 88028, 36320, 14990, 6094, 2154, 614, 128, 1, 2160343, 876852, 357332, 145242, 58468, 21842, 6750, 1714, 256 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Terms obtained by counting with a time-consuming Maple program. Sum of entries in row n = n! = A000142(n). T(n,1) = A180191(n). LINKS Alois P. Heinz, Rows n = 1..18, flattened FORMULA Sum_{k=0..n-1} k * T(n,k) = A018927(n). - Alois P. Heinz, Feb 21 2019 EXAMPLE T(4,2) = 6 because we have 1324, 4132, 2413, 4213, 2431, and 3241. Triangle starts:   1;   1,  1;   1,  3,  2;   1, 13,  6,  4;   1, 67, 30, 14,  8;   ... MAPLE with(combinat): minasc := proc (p) local j, b: for j to nops(p)-1 do if 0 < p[j+1]-p[j] then b[j] := p[j+1]-p[j] else b[j] := infinity end if end do: if min(seq(b[j], j = 1 .. nops(p)-1)) = infinity then 0 else min(seq(b[j], j = 1 .. nops(p)-1)) end if end proc; for n to 10 do P := permute(n): f[n] := sort(add(t^minasc(P[j]), j = 1 .. factorial(n))) end do: for n to 10 do seq(coeff(f[n], t, i), i = 0 .. n-1) end do; # yields sequence in triangular form # second Maple program: b:= proc(s, l, m) option remember; `if`(s={}, x^`if`(m=infinity, 0, m),       add(b(s minus {j}, j, `if`(j (p-> seq(coeff(p, x, i), i=0..n-1))(b({\$1..n}, infinity\$2)): seq(T(n), n=1..10);  # Alois P. Heinz, Feb 21 2019 CROSSREFS Cf. A000142, A018927, A180191. Sequence in context: A068440 A246381 A048647 * A059438 A156628 A104980 Adjacent sequences:  A180187 A180188 A180189 * A180191 A180192 A180193 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Sep 07 2010 STATUS approved

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Last modified October 17 07:57 EDT 2019. Contains 328106 sequences. (Running on oeis4.)