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 A245798 #33 Jan 23 2016 21:51:10 %S A245798 1,1,2,4,12,36,120,360,960,3840,13824,41472,152064,506880,2280960, %T A245798 7983360,29937600,99792000,266112000,1197504000,4790016000, %U A245798 19160064000,73156608000,219469824000,1009561190400,3533464166400,12563428147200,54441521971200,155547205632000 %N A245798 Catalan number analogs for totienomial coefficients (A238453). %C A245798 One definition of the Catalan numbers is binomial(2*n,n) / (n+1); the current sequence models this definition using the generalized binomial coefficients arising from Euler's totient function (A000010). %C A245798 When the INTEGERS (2014) paper was written it was not known that this was an integral sequence (see the final paragraph of that paper). However, it is now known to be integral. %C A245798 Another name could be phi-Catalan numbers. - _Tom Edgar_, Mar 29 2015 %H A245798 Tom Edgar, <a href="/A245798/b245798.txt">Table of n, a(n) for n = 0..28</a> %H A245798 Tom Edgar, <a href="http://www.emis.de/journals/INTEGERS/papers/o62/o62.Abstract.html">Totienomial Coefficients</a>, INTEGERS, 14 (2014), #A62. %H A245798 Tom Edgar and Michael Z. Spivey, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Edgar/edgar3.html">Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers</a>, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6. %F A245798 a(n) = A238453(2*n,n) / A000010(n+1). %e A245798 We see that A238453(10,5) = 72 and A000010(5+1) = 2, so a(5) = (1/2)*72 = 36. %o A245798 (Sage) %o A245798 [(1/euler_phi(n+1))*prod(euler_phi(i) for i in [1..2*n])/prod(euler_phi(i) for i in [1..n])^2 for n in [0..100]] %Y A245798 Cf. A000010, A238453, A000108, A001088. %K A245798 nonn %O A245798 0,3 %A A245798 _Tom Edgar_, Aug 22 2014