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 A386413 #19 Aug 01 2025 17:04:45 %S A386413 1,6,63,792,10935,160056,2438667,38263752,614014830,10029572280, %T A386413 166203389781,2787232297680,47213065271268,806618756189736, %U A386413 13883029872725475,240491818267745760,4189678646994012501,73357895462268102840,1290223574267814268290,22784365638084466567800 %N A386413 G.f. A(x) satisfies A(x) = (1 + 9*x*A(x)^2)^(2/3). %H A386413 Paolo Xausa, <a href="/A386413/b386413.txt">Table of n, a(n) for n = 0..750</a> %H A386413 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a> %F A386413 a(n) = 9^n * binomial((4*n+2)/3,n)/(2*n+1). %F A386413 G.f.: B(x)^2, where B(x) is the g.f. of A078532. %F A386413 D-finite with recurrence n*(n-2)*(n+2)*a(n) -216*(2*n-5)*(4*n-7)*(4*n-1)*a(n-3)=0. - _R. J. Mathar_, Jul 30 2025 %t A386413 A386413[n_] := 9^n*Binomial[(4*n + 2)/3, n]/(2*n + 1); %t A386413 Array[A386413, 25, 0] (* _Paolo Xausa_, Aug 01 2025 *) %o A386413 (PARI) apr(n, p, r) = r*binomial(n*p+r, n)/(n*p+r); %o A386413 a(n) = 9^n*apr(n, 4/3, 2/3); %Y A386413 Cf. A004989, A377269, A386414, A386415. %Y A386413 Cf. A078532, A376636. %K A386413 nonn,easy %O A386413 0,2 %A A386413 _Seiichi Manyama_, Jul 21 2025