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A213280 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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

E. D. Bolker and A. M. Gleason, Counting permutations, J. Combin. Thy., A 29 (1980), 236-242.

EXAMPLE

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],

...

MAPLE

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:

seq(seq(T(n, k), k=1..n), n=1..12);  # Alois P. Heinz, May 14 2016

MATHEMATICA

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}]];

Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, May 26 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A001563 (diagonal of triangle), A213279.

Sequence in context: A049251 A308642 A158674 * A056862 A113035 A099447

Adjacent sequences:  A213277 A213278 A213279 * A213281 A213282 A213283

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jun 08 2012

STATUS

approved

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Last modified February 21 23:41 EST 2020. Contains 332113 sequences. (Running on oeis4.)