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A034001
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One third of triple factorial numbers.
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10
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1, 6, 54, 648, 9720, 174960, 3674160, 88179840, 2380855680, 71425670400, 2357047123200, 84853696435200, 3309294160972800, 138990354760857600, 6254565964238592000, 300219166283452416000, 15311177480456073216000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 495
N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
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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/(1-3x)^2 - Paul Barry (pbarry(AT)wit.ie), Sep 14 2004
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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); ; # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 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); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2009]
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CROSSREFS
| Cf. A007559, A034000.
Sequence in context: A069726 A081132 A158831 * A084062 A137591 A072034
Adjacent sequences: A033998 A033999 A034000 * A034002 A034003 A034004
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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