A108079 a(n) = Sum_{i=0..n} C(2n+i,n+i).

1, 5, 31, 195, 1231, 7798, 49596, 316767, 2031535, 13079352, 84504355, 547707394, 3559971156, 23197272140, 151495214536, 991348425879, 6498704675439, 42669773400220, 280567674704625, 1847219933032320, 12176178948740895, 80346934651630500, 530705476721771520

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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 A365741 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