0,2

a(n-1), n>=1, enumerates increasing plane (aka ordered) trees with n-vertices (one of them a root labeled 1) with one version of a vertex with out-degree r=0 (a leaf or a root) and each vertex with out-degree r>=1 comes in r+2 types (like an (r+2)-ary vertex). See the increasing tree comments under A001498. For example, a(1)=3 from the three trees with n=2 vertices (a root (out-degree r=1, label 1) and a leaf (r=0), label 2). There are three such trees because of the three types of out-degree r=1 vertices. W. Lang Oct 05 2007.

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.

a(n)= 3*A034176(n) = (4*n-1)(!^4), n >= 1, a(0) := 1. E.g.f. (1-4*x)^(-3/4).

a(n) ~ 2^(1/2)*pi^(1/2)*Gamma(3/4)^-1*n^(1/4)*2^(2*n)*e^-n*n^n*{1 - 1/96*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 23 2001

f := n->product( (4*k-1), k=0..n);

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 2, 5!, 4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]

Cf. A004982, A001813, A047053, A051142. a(n)= A000369(n+1, 1) (first column of triangle).

Sequence in context: A074638 A097329 A119097 this_sequence A005373 A078586 A138903

Adjacent sequences: A008542 A008543 A008544 this_sequence A008546 A008547 A008548

nonn,easy,nice

Joe Keane (jgk(AT)jgk.org)