A169958 a(n) = binomial(9*n, n).

1, 9, 153, 2925, 58905, 1221759, 25827165, 553270671, 11969016345, 260887834350, 5720645481903, 126050526132804, 2788629694000605, 61902409203193230, 1378095785451705375, 30756373941461374800, 687917389635036844569, 15415916972482007401455, 346051021610256116115150

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..110

Formula

a(n) = C(9*n-1, n-1)*C(81*n^2, 2)/(3*n*C(9*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 + 8*A(x))^8 + (9^9)*x*A(x)^9 = 0.

Sum_{n >= 1} a(n)*( x*(8*x + 9)^8/(9^9*(1 + x)^9) )^n = x. (End)

Prog

(Magma) [Binomial(9*n, n): n in [0..50] ]; // Vincenzo Librandi, Apr 21 2011

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), A169959 - A169961 (k = 10 thru 12).

Sequence in context: A093849 A165232 A246641 * A012017 A130980 A133309

Adjacent sequences: A169955 A169956 A169957 * A169959 A169960 A169961

Keyword

nonn

Author

N. J. A. Sloane, Aug 07 2010

Status

approved