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A104859
Partial sums of A001764.
17
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
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 24 2005
STATUS
approved