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A101109 Number of sets of lists (sequences) of n labeled elements with k=3 elements per list. 1
1, 0, 0, 6, 0, 0, 360, 0, 0, 60480, 0, 0, 19958400, 0, 0, 10897286400, 0, 0, 8892185702400, 0, 0, 10137091700736000, 0, 0, 15388105201717248000, 0, 0, 30006805143348633600000, 0, 0, 73096577329197271449600000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The (labeled) case for k=2 is A067994, the Hermite numbers. The (labeled) case for k>=1 is A000262, Number of "sets of lists".

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..582

FORMULA

E.g.f.: exp(z^3).

a(0) = 1, a(1) = 0, a(2) = 0, (-n-3)*a(n+3)+3*a(n).

a(n) = n!/(n/3)!, if 3 divides n, 0 otherwise. - Mitch Harris, Jan 19 2006

EXAMPLE

Let Z[i] denote the i-th labeled element. Then a(3) = 6 with the following six sets:

Set(Sequence(Z[3],Z[1],Z[2])), Set(Sequence(Z[2],Z[1],Z[3])), Set(Sequence(Z[3],Z[2],Z[1])), Set(Sequence(Z[2],Z[3],Z[1])), Set(Sequence(Z[1],Z[3],Z[2])), Set(Sequence(Z[1],Z[2],Z[3])).

MAPLE

A101109 := n -> n!*PIECEWISE([1/GAMMA(1/3*n+1), irem(n, 3) = 0], [0, irem(n-1, 3) = 0], [0, irem(n-2, 3) = 0]); [ seq(n!*PIECEWISE([1/GAMMA(1/3*n+1), irem(n, 3) = 0], [0, irem(n-1, 3) = 0], [0, irem(n-2, 3) = 0]), n=0..30) ];

# second Maple program:

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*

       j!*binomial(n-1, j-1), j=`if`(n>2, 3, [][])))

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, May 10 2016

MATHEMATICA

With[{nn=30}, CoefficientList[Series[Exp[x^3], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 16 2013 *)

PROG

(Sage)

def A101109(n) : return factorial(n)/factorial(n/3) if n%3 == 0 else 0

[A101109(n) for n in (0..30)] # Peter Luschny, Jul 12 2012

CROSSREFS

Cf. A000262, A067994.

Sequence in context: A019185 A229510 A230787 * A293526 A293568 A192072

Adjacent sequences:  A101106 A101107 A101108 * A101110 A101111 A101112

KEYWORD

nonn

AUTHOR

Thomas Wieder, Dec 01 2004

STATUS

approved

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Last modified October 20 21:32 EDT 2020. Contains 337910 sequences. (Running on oeis4.)