0,3

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

Starting (1, 4, 28, 280,...) = INVERT transform of A107716: (1, 3, 21,...) [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 22 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=0..100

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

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

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

a(0) := 1, a(n)=(3*n-2)!!! := product(3*k+1, k=0..n-1).

a(n)= 3^n*Pochhammer(1/3, n).

a(n) = Sum_{k=0..n} (-3)^(n-k)*A048994(n, k) .- Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2005

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]

Cf. A001147, A004987, A032031, A008544, A051141. a(n)= A035469(n, 1), n >= 1, (first column of triangle A035469(n, m)).

Cf. A107716 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 22 2009]

Adjacent sequences: A007556 A007557 A007558 this_sequence A007560 A007561 A007562

Sequence in context: A081917 A128318 A032274 this_sequence A138208 A071212 A090353

nonn,nice,easy,new

N. J. A. Sloane (njas(AT)research.att.com).

Better description from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de).