A169959 a(n) = binomial(10*n, n).

1, 10, 190, 4060, 91390, 2118760, 50063860, 1198774720, 28987537150, 706252528630, 17310309456440, 426342151127100, 10542859559688820, 261594860525768000, 6509613950241656640, 162392216278033616560, 4059949873964357469950, 101696990867999141755140

Offset: 0

Author

N. J. A. Sloane, Aug 07 2010

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..115

Crossrefs

binomial(k*n,n): A000984 (k = 2), A005809 (k = 3), A005810 (k = 4), A001449 (k = 5), A004355 (k = 6), A004368 (k = 7), A004381 (k = 8), A169958 - A169961 (k = 9 thru 12).

Programs

Magma

[Binomial(10*n, n): n in [0..50]]; // Vincenzo Librandi, Apr 21 2011

Mathematica

A169959[n_] := Binomial[10*n, n]; Array[A169959, 20, 0] (* Paolo Xausa, Aug 20 2025 *)

Formula

a(n) = C(10*n-1, n-1)*C(100*n^2, 2)/(3*n*C(10*n+1, 3)), n > 0. - Gary Detlefs, Jan 02 2014

From Peter Bala, Feb 21 2022: (Start)

The o.g.f. A(x) is algebraic: (1 - A(x))*(1 + 9*A(x))^9 + (10^10)*x*A(x)^10 = 0.

Sum_{n >= 1} a(n)*( x*(9*x + 10)^9/(10^10*(1 + x)^10) )^n = x. (End)