|
| |
|
|
A104859
|
|
Partial sums of A001764.
|
|
10
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
FORMULA
| a(n)=sum(binomial(3k, k)/(2k+1), k=0..n).
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 8 2011]
|
|
|
MAPLE
| a:=n->sum(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 8 2011]
|
|
|
PROG
| (Maxima) makelist(sum(binomial(3*k, k)/(2*k+1), k, 0, n), n, 0, 20); [Emanuele Munarini, Apr 8 2011]
|
|
|
CROSSREFS
| Cf. A001764
Sequence in context: A101900 A082282 A005967 * A108289 A007779 A084161
Adjacent sequences: A104856 A104857 A104858 * A104860 A104861 A104862
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 24 2005
|
| |
|
|
