A030056 a(n) = binomial(2*n+1, n-6).

1, 15, 136, 969, 5985, 33649, 177100, 888030, 4292145, 20160075, 92561040, 417225900, 1852482996, 8122425444, 35240152720, 151532656696, 646626422970, 2741188875414, 11554258485616, 48459472266975

Offset: 6

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 6..500
• Milan Janjic, Two Enumerative Functions.

Crossrefs

Diagonal 14 of triangle A100257.

Cf. A001622.

Programs

Mathematica

Table[Binomial[2*n + 1, n - 6], {n, 6, 25}] (* Amiram Eldar, Jan 24 2022 *)

Python

from _future_ import division
A030056_list, b = [], 1
for n in range(6,501):
    A030056_list.append(b)
    b = b*(2*n+2)*(2*n+3)//((n-5)*(n+8)) # Chai Wah Wu, Jan 26 2016

Formula

a(n+1) = a(n)*(2*n+2)*(2*n+3)/((n-5)*(n+8)). - Chai Wah Wu, Jan 26 2016

From Amiram Eldar, Jan 24 2022: (Start)

Sum_{n>=6} 1/a(n) = 40*Pi/(9*sqrt(3)) - 96827/13860.

Sum_{n>=6} (-1)^n/a(n) = 29248*log(phi)/(5*sqrt(5)) - 3486955/2772, where phi is the golden ratio (A001622). (End)