OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = Sum_{k=0..n} binomial(3k, k)/(2k+1).
G.f.: T(z)/(1-z), where T = 1+z*T^3.
G.f.: 2*sin((1/3)*arcsin(sqrt(27*z/4)))/((1-z)*sqrt(3*z)).
Recurrence: 2*(2*n^2 + 9*n + 10)*a(n+2) - (31*n^2 + 99*n + 80)*a(1+n) + 3*(9*n^2 + 27*n + 20)*a(n) = 0. - Emanuele Munarini, Apr 08 2011
a(n) ~ 3^(3*n+7/2)/(23*sqrt(Pi)*2^(2*n+2)*n^(3/2)). - Vaclav Kotesovec, Oct 17 2012
G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x * (1 - x)^2 * A(x)^3. - Ilya Gutkovskiy, Jul 25 2021
MAPLE
a:=n->add(binomial(3*k, k)/(2*k+1), k=0..n): seq(a(n), n=0..26);
MATHEMATICA
Table[Sum[Binomial[3k, k]/(2k+1), {k, 0, n}], {n, 0, 20}] (* Emanuele Munarini, Apr 08 2011 *)
PROG
(Maxima) makelist(sum(binomial(3*k, k)/(2*k+1), k, 0, n), n, 0, 20); /* Emanuele Munarini, Apr 08 2011 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 24 2005
STATUS
approved