A196789 Binomial coefficients C(2*n+10,10).

1, 66, 1001, 8008, 43758, 184756, 646646, 1961256, 5311735, 13123110, 30045015, 64512240, 131128140, 254186856, 472733756, 847660528, 1471442973, 2481256778, 4076350421, 6540715896, 10272278170, 15820024220, 23930713170, 35607051480, 52179482355, 75394027566

Offset: 0

Author

Vincenzo Librandi, Oct 07 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A002299, A053134, A053135, A053136, A053137, A053138.

Programs

Magma

[Binomial(2*n+10,10): n in [0..30]];

Mathematica

a[n_] := Binomial[2*n + 10, 10]; Array[a, 20, 0] (* Amiram Eldar, Oct 21 2022 *)

Formula

G.f.: (11*x^5+165*x^4+462*x^3+330*x^2+55*x+1) / (1-x)^11.

From Amiram Eldar, Oct 21 2022: (Start)

Sum_{n>=0} 1/a(n) = 2560*log(2) - 148969/84.

Sum_{n>=0} (-1)^n/a(n) = 40*Pi - 80*log(2) - 5815/84. (End)