A030055 a(n) = binomial(2*n+1, n-5).

1, 13, 105, 680, 3876, 20349, 100947, 480700, 2220075, 10015005, 44352165, 193536720, 834451800, 3562467300, 15084504396, 63432274896, 265182149218, 1103068603890, 4568648125690, 18851684897584

Offset: 5

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 5..1000
• Milan Janjic, Two Enumerative Functions.

Crossrefs

Diagonal 12 of triangle A100257.

Cf. A001622.

Programs

GAP

List([5..25],n->Binomial(2*n+1,n-5)); # Muniru A Asiru, Oct 24 2018

Magma

[Binomial(2*n+1, n-5): n in [5..30]]; // G. C. Greubel, Oct 23 2018

Maple

seq(binomial(2*n+1,n-5),n=5..25); # Muniru A Asiru, Oct 24 2018

Mathematica

Table[Binomial[2*n+1, n-5], {n, 5, 30}] (* G. C. Greubel, Oct 23 2018 *)

PARI

vector(30, n, m=n+4; binomial(2*m+1,m-5)) \\ Michel Marcus, Aug 11 2015

Formula

G.f.: x^5*2048/((1-sqrt(1-4*x))^11*sqrt(1-4*x))+(-1/x^6+9/x^5-28/x^4+35/x^3-15/x^2+1/x). - Vladimir Kruchinin, Aug 11 2015

From Amiram Eldar, Jan 24 2022: (Start)

Sum_{n>=5} 1/a(n) = 9497/1260 - 32*Pi/(9*sqrt(3)).

Sum_{n>=5} (-1)^(n+1)/a(n) = 9392*log(phi)/(5*sqrt(5)) - 508169/1260, where phi is the golden ratio (A001622). (End)