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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). 1
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

Table of n, a(n) for n=1..55.

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

CROSSREFS

Cf. A000142, 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 February 19 17:00 EST 2019. Contains 320311 sequences. (Running on oeis4.)