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A104859 Partial sums of A001764. 11
1, 2, 5, 17, 72, 345, 1773, 9525, 52788, 299463, 1730178, 10144818, 60211926, 361042498, 2183809018, 13308564682, 81637319641, 503667864976, 3123298907641, 19456221197941, 121696331095636, 764008782313381 (list; graph; refs; listen; history; text; internal format)
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: A336282 A082282 A005967 * A108289 A007779 A084161

Adjacent sequences:  A104856 A104857 A104858 * A104860 A104861 A104862

KEYWORD

nonn,easy,changed

AUTHOR

Emeric Deutsch, Apr 24 2005

STATUS

approved

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Last modified August 2 12:47 EDT 2021. Contains 346424 sequences. (Running on oeis4.)