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 A004321 #43 Jan 14 2025 10:34:57
%S A004321 1,12,105,816,5985,42504,296010,2035800,13884156,94143280,635745396,
%T A004321 4280561376,28760021745,192928249296,1292706174900,8654327655120,
%U A004321 57902201338905,387221678682300,2588713818544245
%N A004321 Binomial coefficient C(3n, n-3).
%D A004321 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
%H A004321 Michael De Vlieger, <a href="/A004321/b004321.txt">Table of n, a(n) for n = 3..1209</a>
%H A004321 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A004321 Alin Bostan, Frédéric Chyzak, and Vincent Pilaud, <a href="https://arxiv.org/abs/2303.10986">Refined product formulas for Tamari intervals</a>, arXiv:2303.10986 [math.CO], 2023.
%H A004321 Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>
%H A004321 Daniel W. Stasiuk, <a href="http://hdl.handle.net/10388/11865">An Enumeration Problem for Sequences of n-ary Trees Arising from Algebraic Operads</a>, Master's Thesis, University of Saskatchewan-Saskatoon (2018).
%F A004321 From _Ilya Gutkovskiy_, Jan 31 2017: (Start)
%F A004321 E.g.f.: (1/6)*x^3*2F2(10/3,11/3; 5,11/2; 27*x/4).
%F A004321 a(n) ~ 3^(3*n+1/2)/(sqrt(Pi*n)*4^(n+2)). (End)
%F A004321 D-finite with recurrence -2*(2*n+3)*(n-3)*(n+1)*a(n) +3*n*(3*n-1)*(3*n-2)*a(n-1)=0. - _R. J. Mathar_, Jan 13 2025
%p A004321 a:=n->sum(binomial(2*n-2,n+j)*binomial(n-1,n-j+1),j=0..n): seq(a(n), n=4..22); # _Zerinvary Lajos_, Jan 29 2007
%t A004321 Table[Binomial[3n, n-3], {n,3,30}] (* _Wesley Ivan Hurt_, Feb 04 2014 *)
%o A004321 (PARI) {a(n) = binomial(3*n, n-3)}; \\ _G. C. Greubel_, Mar 21 2019
%o A004321 (Magma) [Binomial(3*n,n-3): n in [3..30]]; // _G. C. Greubel_, Mar 21 2019
%o A004321 (Sage) [binomial(3*n,n-3) for n in (3..30)] # _G. C. Greubel_, Mar 21 2019
%o A004321 (GAP) List([3..30], n-> Binomial(3*n,n-3)); # _G. C. Greubel_, Mar 21 2019
%Y A004321 Cf. binomial(k*n, n-k): A000027 (k=1), A002694 (k=2), this sequence (k=3), A004334 (k=4), A004347 (k=5), A004361 (k=6), A004375 (k=7), A004389 (k=8), A281580 (k=9).
%K A004321 nonn,easy
%O A004321 3,2
%A A004321 _N. J. A. Sloane_