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A110520 Expansion of 1/(1-2*x*c(3*x)), c(x) the g.f. of A000108. 6
1, 2, 10, 68, 538, 4652, 42628, 406856, 4001914, 40285724, 413049580, 4298523704, 45288486436, 482122686008, 5178044596168, 56038403289488, 610508962548538, 6690154684006268, 73693477140179548, 815508203755227608 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of number triangle A110519.

Hankel transform is A135397. Hankel transform of the aerated sequence is A083667. [From Paul Barry, Sep 15 2009]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

J. Abate, 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<=k<=n} A039599(n,k)*(-1)^k*3^(n-k). - Philippe Deléham, Dec 11 2007

a(n)=Sum_{k, 0<=k<=n} A094385(n,k)*2^k. [From Philippe Deléham, Feb 26 2009]

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,...

...

- Gary W. Adamson, Jul 12 2011

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

Sequence in context: A152621 A147725 A074603 * A136633 A082580 A231492

Adjacent sequences:  A110517 A110518 A110519 * A110521 A110522 A110523

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 24 2005

STATUS

approved

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Last modified October 15 22:21 EDT 2018. Contains 316252 sequences. (Running on oeis4.)