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A317132 Number of permutations of [n] whose lengths of increasing runs are factorials. 7
1, 1, 2, 5, 17, 70, 350, 2029, 13495, 100813, 837647, 7652306, 76282541, 823684964, 9578815164, 119346454671, 1586149739684, 22397700381817, 334879465463998, 5285103821004717, 87800206978975107, 1531533620821692217, 27987305231654121046, 534688325008397289484 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

FORMULA

a(3) = 5: 132, 213, 231, 312, 321.

a(4) = 17: 1324, 1423, 1432, 2143, 2314, 2413, 2431, 3142, 3214, 3241, 3412, 3421, 4132, 4213, 4231, 4312, 4321.

MAPLE

g:= proc(n) local i; 1; for i from 2 do

      if n=% then 1; break elif n<% then 0; break fi;

      %*i od; g(n):=%

    end:

b:= proc(u, o, t) option remember; `if`(u+o=0, g(t),

      `if`(g(t)=1, add(b(u-j, o+j-1, 1), j=1..u), 0)+

       add(b(u+j-1, o-j, t+1), j=1..o))

    end:

a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):

seq(a(n), n=0..27);

CROSSREFS

Cf. A000142, A097597, A272603, A317111, A317128, A317129, A317130, A317131, A317448.

Sequence in context: A263642 A263682 A049774 * A335926 A139402 A143382

Adjacent sequences:  A317129 A317130 A317131 * A317133 A317134 A317135

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 21 2018

STATUS

approved

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Last modified September 24 07:28 EDT 2020. Contains 337317 sequences. (Running on oeis4.)