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A213280
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Triangle read by rows: T(n,k) (n>=1, 1 <= k <= n) = number of permutations of [1..n] in which none of the cycle lengths are divisible by k.
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2
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0, 0, 1, 0, 3, 4, 0, 9, 16, 18, 0, 45, 80, 90, 96, 0, 225, 400, 540, 576, 600, 0, 1575, 2800, 3780, 4032, 4200, 4320, 0, 11025, 22400, 26460, 32256, 33600, 34560, 35280, 0, 99225, 179200, 238140, 290304, 302400, 311040, 317520, 322560, 0, 893025, 1792000, 2381400, 2612736, 3024000, 3110400, 3175200, 3225600, 3265920
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graph;
refs;
listen;
history;
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OFFSET
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1,5
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LINKS
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EXAMPLE
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Triangle begins
[0],
[0, 1],
[0, 3, 4],
[0, 9, 16, 18],
[0, 45, 80, 90, 96],
[0, 225, 400, 540, 576, 600],
[0, 1575, 2800, 3780, 4032, 4200, 4320],
[0, 11025, 22400, 26460, 32256, 33600, 34560, 35280],
[0, 99225, 179200, 238140, 290304, 302400, 311040, 317520, 322560],
[0, 893025, 1792000, 2381400, 2612736, 3024000, 3110400, 3175200, 3225600, 3265920],
[0, 9823275, 19712000, 26195400, 28740096, 33264000, 34214400, 34927200, 35481600, 35925120, 36288000],
[0, 108056025, 216832000, 288149400, 344881152, 365904000, 410572800, 419126400, 425779200, 431101440, 435456000, 439084800],
...
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MAPLE
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read transforms;
f:=(n, d)->mul(j-did(j, d), j=1..n); # did(d, j) = 1 iff j divides d, otherwise 0
g:=n->[seq(f(n, d), d=1..n)];
[seq(g(n), n=1..14)];
# second Maple program:
T:= proc(n, k) option remember; `if`(n=0, 1, add(
`if`(irem(j, k)=0, 0, binomial(n-1, j-1)*(j-1)!*
T(n-j, k)), j=1..n))
end:
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MATHEMATICA
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T[n_, k_] := T[n, k] = If[n == 0, 1, Sum[If[Mod[j, k] == 0, 0, Binomial[n - 1, j - 1]*(j - 1)!*T[n - j, k]], {j, 1, n}]];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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