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 A384680 #11 Jun 07 2025 08:21:35 %S A384680 1,1,3,15,100,805,7442,76750,866818,10586499,138549918,1929878820, %T A384680 28459172110,442421488758,7225177328165,123586748434192, %U A384680 2208493015533530,41138303109509415,797178212982793708,16041390159326400966,334654194086236031816,7227174934846895031544 %N A384680 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)*A(x*A(x)^3) ). %F A384680 See A384681. %t A384680 terms = 22; A[_] = 0; Do[A[x_] = 1/(1-x*A[x]*A[x*A[x]^3]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jun 07 2025 *) %o A384680 (PARI) a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-j+k, j)/(3*n-j+k)*a(n-j, j))); %Y A384680 Column k=1 of A384681. %Y A384680 Cf. A143501, A215505, A384145. %K A384680 nonn %O A384680 0,3 %A A384680 _Seiichi Manyama_, Jun 06 2025