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 A387091 #23 Aug 20 2025 10:28:49
%S A387091 1,10,171,3276,66045,1370754,28989675,621216192,13442126049,
%T A387091 293052087900,6426898010533,141629804643600,3133614810784185,
%U A387091 69566517009302868,1548833316392624625,34569147570568156800,773240476721553042345,17328840976366636057110
%N A387091 a(n) = binomial(9*n+1,n).
%H A387091 Paolo Xausa, <a href="/A387091/b387091.txt">Table of n, a(n) for n = 0..700</a>
%F A387091 a(n) = Sum_{k=0..n} binomial(9*n-k,n-k).
%F A387091 G.f.: 1/(1 - x*g^7*(9+g)) where g = 1+x*g^9 is the g.f. of A062994.
%F A387091 G.f.: g^2/(9-8*g) where g = 1+x*g^9 is the g.f. of A062994.
%F A387091 G.f.: B(x)^2/(1 + 8*(B(x)-1)/9), where B(x) is the g.f. of A169958.
%F A387091 D-finite with recurrence +128*n*(8*n-5)*(4*n-1)*(8*n+1)*(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+1)*(3*n-2)*(9*n-4)*(9*n-2)*a(n-1)=0. - _R. J. Mathar_, Aug 19 2025
%F A387091 a(n) ~ 3^(18*n+3) / (sqrt(Pi*n) * 2^(24*n+5)). - _Vaclav Kotesovec_, Aug 20 2025
%t A387091 A387091[n_] := Binomial[9*n + 1, n]; Array[A387091, 20, 0] (* _Paolo Xausa_, Aug 20 2025 *)
%o A387091 (PARI) a(n) = binomial(9*n+1, n);
%Y A387091 Cf. A001700, A045721, A052203, A079589, A079590.
%Y A387091 Cf. A062994, A169958.
%K A387091 nonn,easy
%O A387091 0,2
%A A387091 _Seiichi Manyama_, Aug 16 2025