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A317132
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Number of permutations of [n] whose lengths of increasing runs are factorials.
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7
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1, 1, 2, 5, 17, 70, 350, 2029, 13495, 100813, 837647, 7652306, 76282541, 823684964, 9578815164, 119346454671, 1586149739684, 22397700381817, 334879465463998, 5285103821004717, 87800206978975107, 1531533620821692217, 27987305231654121046, 534688325008397289484
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OFFSET
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0,3
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LINKS
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FORMULA
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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.
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MAPLE
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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);
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MATHEMATICA
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g[n_] := g[n] = Module[{i, k = 1}, For[i = 2, True, i++,
If[n == k, k = 1; Break[]]; If[n < k, k = 0; Break[]];
k = k*i]; k];
b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, g[t],
If[g[t] == 1, Sum[b[u - j, o + j - 1, 1], {j, 1, u}], 0] +
Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}]];
a[n_] := If[n == 0, 1, Sum[b[j - 1, n - j, 1], {j, 1, n}]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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