OFFSET
0,2
COMMENTS
3-fold convolution of A002212. - Emeric Deutsch, Mar 13 2004
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
S. J. Cyvin et al., Enumeration and classification of certain polygonal systems representing polycyclic conjugated hydrocarbons: annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.
FORMULA
G.f.: (1 - x - sqrt(1-6*x+5*x^2))^3/(8*x^3). - Emeric Deutsch, Mar 13 2004
a(n) = (3/n)*Sum_{j=1..n} binomial(n, j)*binomial(2j+2, j-1) for n >= 1. - Emeric Deutsch, Mar 25 2004
Recurrence: (n+2)*(n+3)*a(n) = 2*(n+2)*(3*n+4)*a(n-1) - 5*(n-2)*(n+3)*a(n-2). - Vaclav Kotesovec, Oct 08 2012
a(n) ~ 6*5^(n+1/2)/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 08 2012
MAPLE
a := n->(3/n)*sum(binomial(n, j)*binomial(2*j+2, j-1), j=1..n): 1, seq(a(n), n=1..22);
MATHEMATICA
a[n_] := 3*(Hypergeometric2F1[5/2, 1-n, 5, -4] + (n-1)*Hypergeometric2F1[7/2, 2-n, 6, -4]); a[0]=1; Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Jun 13 2012, after Emeric Deutsch *)
CoefficientList[Series[(1-x-Sqrt[1-6x+5x^2])^3/(8x^3), {x, 0, 30}], x] (* Harvey P. Dale, Feb 07 2015 *)
PROG
(PARI) x='x+O('x^66); Vec((1-x-sqrt(1-6*x+5*x^2))^3/(8*x^3)) \\ Joerg Arndt, May 04 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, Mar 13 2004
STATUS
approved