This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A169958 #36 Aug 20 2025 10:39:58
%S A169958 1,9,153,2925,58905,1221759,25827165,553270671,11969016345,
%T A169958 260887834350,5720645481903,126050526132804,2788629694000605,
%U A169958 61902409203193230,1378095785451705375,30756373941461374800,687917389635036844569,15415916972482007401455,346051021610256116115150
%N A169958 a(n) = binomial(9*n, n).
%H A169958 Vincenzo Librandi, <a href="/A169958/b169958.txt">Table of n, a(n) for n = 0..110</a>
%F A169958 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
%F A169958 From _Peter Bala_, Feb 21 2022: (Start)
%F A169958 The o.g.f. A(x) is algebraic: (1 - A(x))*(1 + 8*A(x))^8 + (9^9)*x*A(x)^9 = 0.
%F A169958 Sum_{n >= 1} a(n)*( x*(8*x + 9)^8/(9^9*(1 + x)^9) )^n = x. (End)
%F A169958 D-finite with recurrence 128*n*(8*n-5) *(4*n-1) *(8*n-7) *(2*n-1) *(8*n-1) *(4*n-3) *(8*n-3)*a(n) -81*(9*n-7) *(9*n-5) *(3*n-1) *(9*n-1) *(9*n-8) *(3*n-2) *(9*n-4) *(9*n-2)*a(n-1)=0. - _R. J. Mathar_, Aug 19 2025
%F A169958 G.f.: 8F7(8/9, 7/9, 2/3, 5/9, 4/9, 1/3, 2/9 ,1/9 ; 7/8, 3/4, 5/8, 1/2, 3/8, 1/4, 1/8; 387420489/16777216*x). - _R. J. Mathar_, Aug 19 2025
%t A169958 A169958[n_] := Binomial[9*n, n]; Array[A169958, 20, 0] (* _Paolo Xausa_, Aug 20 2025 *)
%o A169958 (Magma) [Binomial(9*n, n): n in [0..50] ]; // _Vincenzo Librandi_, Apr 21 2011
%Y A169958 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).
%K A169958 nonn
%O A169958 0,2
%A A169958 _N. J. A. Sloane_, Aug 07 2010