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A300613 Number of partitions of the n-dimensional hypercube resulting from a sequence of n n-sections, each of which divides any part perpendicular to any of the axes. 2
1, 1, 8, 324, 35840, 7906250, 2931489792, 1645181968584, 1302784779485184, 1384565648740109550, 1902231808400000000000, 3281726715984295577534536, 6946466406905591840863420416, 17702487251379919853870809258728, 53467000591059566447137539120168960 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..25

EXAMPLE

a(2) = 8:

  ._______.  ._______.  ._______.  ._______.

  | | |   |  |   | | |  |_______|  |       |

  | | |   |  |   | | |  |_______|  |_______|

  | | |   |  |   | | |  |       |  |_______|

  |_|_|___|  |___|_|_|  |_______|  |_______|

  ._______.  ._______.  ._______.  ._______.

  |   |   |  |   |   |  |   |   |  |       |

  |___|   |  |   |___|  |___|___|  |_______|

  |   |   |  |   |   |  |       |  |   |   |

  |___|___|  |___|___|  |_______|  |___|___|.

MAPLE

a:= proc(n) option remember; `if`(n<2, 1, coeff(series(

      RootOf(x*(-1)^n=add(binomial(n, i)*(G*x)^(n^(n-i))*

       (-1)^i, i=0..n), G), x, n^2-n+1), x, n^2-n))

    end:

seq(a(n), n=0..12);

# second Maple program:

b:= proc(n, k, t, d) option remember; `if`(t=0, 1, `if`(t=1,

      g(n-1, k, d), add(g(j, k, d)*b(n-j-1, k, t-1, d), j=0..n-2)))

    end:

g:= proc(n, k, d) option remember; `if`(n=0, 1,

      -add(binomial(k, j)*(-1)^j*b(n+1, k, d^j, d), j=1..k))

    end:

a:= n-> g(n^2-n, n$2):

seq(a(n), n=0..14);

MATHEMATICA

b[n_, k_, t_, d_] := b[n, k, t, d] = If[t == 0, 1, If[t == 1, g[n - 1, k, d], Sum[g[j, k, d] b[n - j - 1, k, t - 1, d], {j, 0, n - 2}]]];

g[n_, k_, d_] := g[n, k, d] = If[n == 0, 1, -Sum[Binomial[k, j] (-1)^j b[n + 1, k, d^j, d], {j, 1, k}]];

a[n_] := g[n^2 - n, n, n];

Table[Print[n, " ", a[n]]; a[n], {n, 0, 14}] (* Jean-François Alcover, Dec 30 2018, from second Maple program *)

CROSSREFS

Cf. A300474.

Sequence in context: A171248 A344094 A264053 * A221407 A204069 A226551

Adjacent sequences:  A300610 A300611 A300612 * A300614 A300615 A300616

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 15 2018

STATUS

approved

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Last modified July 24 03:29 EDT 2021. Contains 346273 sequences. (Running on oeis4.)