login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A108079 a(n) = Sum_{i=0..n} C(2n+i,n+i). 0
1, 5, 31, 195, 1231, 7798, 49596, 316767, 2031535, 13079352, 84504355, 547707394, 3559971156, 23197272140, 151495214536, 991348425879, 6498704675439, 42669773400220, 280567674704625, 1847219933032320, 12176178948740895, 80346934651630500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = binomial(3*n+1,n+1)-binomial(2*n,n-1). - Zerinvary Lajos, May 11 2006, corrected by Robert Israel, Oct 01 2015

G.f.: x*(1/x-1/B(x))'+x*B'(x)/B(x)-x*C'(x), where B(x)+1 is g.f of A001764, C(x) is g.f. of A000108. - Vladimir Kruchinin, Oct 01 2015

MATHEMATICA

Table[Binomial[3 n + 1, n + 1] - Binomial[2 n, n - 1], {n, 0, 40}] (* Vincenzo Librandi, Oct 02 2015 *)

PROG

(Maxima)

B(x):=(2/sqrt(3*x))*sin((1/3)*asin(sqrt(27*x/4)))-1;

C(x):=(1-sqrt(1-4*x))/(2*x);

taylor(x*diff(1/x-1/B(x), x)+x*diff(B(x), x)/B(x)-x*diff(C(x), x), x, 0, 10); /* Vladimir Kruchinin, Oct 01 2015 */

(Magma) [Binomial(3*n+1, n+1)-Binomial(2*n, n-1): n in [0..25]]; // Vincenzo Librandi, Oct 02 2015

(PARI) a(n) = binomial(3*n+1, n+1)-binomial(2*n, n-1);

vector (100, n, a(n-1)) \\ Altug Alkan, Oct 01 2015

CROSSREFS

Cf. A000108, A001791, A001764.

Sequence in context: A015540 A014987 A343496 * A164038 A260782 A084235

Adjacent sequences: A108076 A108077 A108078 * A108080 A108081 A108082

KEYWORD

nonn

AUTHOR

Ralf Stephan, Jun 03 2005

EXTENSIONS

More terms from Vincenzo Librandi, Oct 02 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 07:38 EST 2022. Contains 358691 sequences. (Running on oeis4.)