OFFSET
0,2
COMMENTS
Row sums of number triangle A110519.
Hankel transform is A135397. Hankel transform of the aerated sequence is A083667. - Paul Barry, Sep 15 2009
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
J. Abate and W. Whitt, Brownian Motion and the Generalized Catalan Numbers, J. Int. Seq. 14 (2011) # 11.2.6, example section 3.
FORMULA
a(0)=1, a(n) = Sum_{k=0..n} Sum_{j=0..n} j*C(2n-j-1, n-j)*C(j, k)*3^(n-j)/n, n > 0.
a(n) = Sum_{k=0..n} A039599(n,k)*(-1)^k*3^(n-k). - Philippe Deléham, Dec 11 2007
a(n) = Sum_{k=0..n} A094385(n,k)*2^k. - Philippe Deléham, Feb 26 2009
From Gary W. Adamson, Jul 12 2011: (Start)
a(n) = the top left term in M^n, M = the infinite square production matrix:
2, 2, 0, 0, 0, 0, ...
3, 3, 3, 0, 0, 0, ...
3, 3, 3, 3, 0, 0, ...
3, 3, 3, 3, 3, 0, ...
3, 3, 3, 3, 3, 3, ...
... (End)
n*a(n) + 2*(9-4*n)*a(n-1) + 24*(3-2*n)*a(n-2) = 0. - R. J. Mathar, Nov 14 2011
a(n) ~ 3*12^n/(8*sqrt(Pi)n^(3/2)). - Vaclav Kotesovec, Oct 18 2012
MATHEMATICA
Flatten[{1, Table[Sum[Sum[j*Binomial[2n-j-1, n-j]*Binomial[j, k]*3^(n-j)/n, {j, 0, n}], {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 18 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 24 2005
STATUS
approved