A104859 Partial sums of A001764.

1, 2, 5, 17, 72, 345, 1773, 9525, 52788, 299463, 1730178, 10144818, 60211926, 361042498, 2183809018, 13308564682, 81637319641, 503667864976, 3123298907641, 19456221197941, 121696331095636, 764008782313381

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

Cf. A001764.

Sequence in context: A082282 A005967 A369402 * A108289 A007779 A084161

Adjacent sequences: A104856 A104857 A104858 * A104860 A104861 A104862

Keyword

nonn,easy

Author

Emeric Deutsch, Apr 24 2005

Status

approved