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 A004117 #34 Jan 19 2025 14:36:09
%S A004117 1,1,2,14,35,91,728,1976,5434,135850,380380,1071980,9111830,25933670,
%T A004117 74096200,637227320,1832028545,5280552865,137294374490,397431084050,
%U A004117 1152550143745,10043651252635,29217894553120,85112997176480
%N A004117 Numerators of expansion of (1-x)^(-1/3).
%C A004117 For n >= 1, a(n) is also the numerator of beta(n+1/3,2/3)*sqrt(27)/(2*Pi). - _Groux Roland_, May 17 2011
%H A004117 Vincenzo Librandi, <a href="/A004117/b004117.txt">Table of n, a(n) for n = 0..1000</a>
%H A004117 Paveł Szabłowski, <a href="https://cdm.ucalgary.ca/article/view/76214">Beta distributions whose moment sequences are related to integer sequences listed in the OEIS</a>, Contrib. Disc. Math. (2024) Vol. 19, No. 4, 85-109. See p. 93.
%F A004117 (1/n!) * 3^A054861(n) * Product_{k=0..n-1} (3k+1). - _Ralf Stephan_, Mar 13 2004
%F A004117 Numerators in (1-3t)^(-1/3) = 1 + t + 2*t^2 + (14/3)*t^3 + (35/3)*t^4 + (91/3)*t^5 + (728/9)*t^6 + (1976/9)*t^7 + (5434/9)*t^8 + ... = 1 + t + 4*t^2/2! + 28*t^3/3! + 280*t^4/4! + 3640*t^5/5! + 58240*t^6/6! + ... = e.g.f. for triple factorials A007559 (cf. A094638). - _Tom Copeland_, Dec 04 2013
%t A004117 Table[Numerator[Binomial[-1/3,n] (-1)^n],{n,0,40}] (* _Vincenzo Librandi_, Jun 13 2012 *)
%o A004117 (PARI) a(n)=prod(k=1,n,3*k-2)/n!*3^sum(k=1,n,valuation(k,3))
%Y A004117 Cf. A004128.
%Y A004117 Cf. A004987, A007559, A047657, A054861, A034689, A053101, A072888.
%K A004117 nonn
%O A004117 0,3
%A A004117 _N. J. A. Sloane_
%E A004117 Typo in formula fixed by _Pontus von Brömssen_, Nov 25 2008