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A034001 One third of triple factorial numbers. 13
1, 6, 54, 648, 9720, 174960, 3674160, 88179840, 2380855680, 71425670400, 2357047123200, 84853696435200, 3309294160972800, 138990354760857600, 6254565964238592000, 300219166283452416000, 15311177480456073216000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..100

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 495

Norihiro Nakashima, Shuhei Tsujie, Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species, arXiv:1904.09748 [math.CO], 2019.

N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, arXiv:math/0307064 [math.CO], 2003; Order 21 (2004), 83-89.

FORMULA

3*a(n) = (3*n)!!! := product(3*j, j=1..n) = 3^n*n!.

E.g.f.: (-1 + 1/(1-3*x))/3.

E.g.f.: 1/(1-3*x)^2. - Paul Barry, Sep 14 2004. For offset 0. -Wolfdieter Lang, Apr 06 2017

D-finite with recurrence a(n) - 3*n*a(n-1)=0. - R. J. Mathar, Dec 02 2012

MAPLE

with(combstruct); SeqSeqSeqL := [T, {T=Sequence(S), S=Sequence(U, card >= 1), U=Sequence(Z, card >=1)}, labeled]; seq(count(SeqSeqSeqL, size=j), j=1..12);

with(combstruct): SeqSeqSeqL := [T, {T=Sequence(S), S=Sequence(U, card >= 1), U=Sequence(Z, card >=1)}, labeled]: seq(count(SeqSeqSeqL, size=j), j=1..17); # Zerinvary Lajos, Apr 04 2009

restart: G(x):=(1-3*x)^(n-3): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1], x) od:x:=0:seq(f[n], n=0..16); # Zerinvary Lajos, Apr 04 2009

MATHEMATICA

terms = 17;

CoefficientList[1/(1-3x)^2 + O[x]^terms, x] Range[0, terms-1]! (* Jean-Fran├žois Alcover, Jul 28 2018 *)

Table[3^(n-1)*n!, {n, 20}] (* G. C. Greubel, Aug 15 2019 *)

PROG

(GAP) List([1..20], n->3^(n-1)*Factorial(n)); # Muniru A Asiru, Jul 28 2018

(PARI) vector(20, n, 3^(n-1)*n!) \\ G. C. Greubel, Aug 15 2019

(MAGMA) [3^(n-1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 15 2019

(Sage) [3^(n-1)*factorial(n) for n in (1..20)] # G. C. Greubel, Aug 15 2019

CROSSREFS

Cf. A007559, A034000.

Sequence in context: A305602 A081132 A158831 * A084062 A292633 A137591

Adjacent sequences:  A033998 A033999 A034000 * A034002 A034003 A034004

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)