%I A007559 M3627
%S A007559 1,1,4,28,280,3640,58240,1106560,24344320,608608000,17041024000,
%T A007559 528271744000,17961239296000,664565853952000,26582634158080000,
%U A007559 1143053268797440000,52580450364682240000,2576442067869429760000
%N A007559 Triple factorial numbers (3*n-2)!!! with leading 1 added.
%C A007559 a(n) = number of increasing quaternary trees on n vertices. (See A001147 
               for ternary and A000142 for binary trees.) - David Callan (callan(AT)stat.wisc.edu), 
               Mar 30 2007
%C A007559 Starting (1, 4, 28, 280,...) = INVERT transform of A107716: (1, 3, 21,
               ...) [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 22 2009]
%D A007559 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007559 T. D. Noe, <a href="b007559.txt">Table of n, a(n) for n=0..100</a>
%H A007559 W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               On generalizations of Stirling number triangles</a>, J. Integer Seqs., 
               Vol. 3 (2000), #00.2.4.
%F A007559 E.g.f.: (1-3*x)^(-1/3).
%F A007559 a(n) ~ 2^(1/2)*pi^(1/2)*Gamma(1/3)^-1*n^(-1/6)*3^n*e^-n*n^n*{1 - 1/36*n^-1 
               - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 22 2001
%F A007559 a(0) := 1, a(n)=(3*n-2)!!! := product(3*k+1, k=0..n-1).
%F A007559 a(n)= 3^n*Pochhammer(1/3, n).
%F A007559 a(n) = Sum_{k=0..n} (-3)^(n-k)*A048994(n, k) .- Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Oct 29 2005
%p A007559 restart: G(x):=(1-3*x)^(-1/3): 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..17);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 03 2009]
%Y A007559 Cf. A001147, A004987, A032031, A008544, A051141. a(n)= A035469(n, 1), 
               n >= 1, (first column of triangle A035469(n, m)).
%Y A007559 Cf. A107716 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 22 2009]
%Y A007559 Sequence in context: A081917 A128318 A032274 this_sequence A138208 A071212 
               A090353
%Y A007559 Adjacent sequences: A007556 A007557 A007558 this_sequence A007560 A007561 
               A007562
%K A007559 nonn,nice,easy
%O A007559 0,3
%A A007559 N. J. A. Sloane (njas(AT)research.att.com).
%E A007559 Better description from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de).