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 A386416 #16 Aug 01 2025 17:04:42 %S A386416 1,3,63,1881,65610,2499336,100777122,4228144596,182674383705, %T A386416 8072369224920,363154406671485,16576444298006658,765806677899249168, %U A386416 35739548618003938440,1682429522012566325460,79793991407758199002740,3809208342822290233767522,182890356905449116974950200 %N A386416 G.f. A(x) satisfies A(x) = (1 + 9*x*A(x)^8)^(1/3). %H A386416 Paolo Xausa, <a href="/A386416/b386416.txt">Table of n, a(n) for n = 0..550</a> %H A386416 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a> %F A386416 a(n) = 9^n * binomial((8*n+1)/3,n)/(8*n+1). %F A386416 G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^13). %F A386416 D-finite with recurrence 5*n*(n-1)*(n-2)*(5*n-8)*(5*n-11)*(5*n+1)*(5*n-2)*a(n) -3456*(8*n-11)*(8*n-5)*(4*n-1)*(8*n-23)*(2*n-5)*(8*n-17)*(4*n-7)*a(n-3)=0. - _R. J. Mathar_, Jul 30 2025 %t A386416 A386416[n_] := 9^n*Binomial[(8*n + 1)/3, n]/(8*n + 1); %t A386416 Array[A386416, 20, 0] (* _Paolo Xausa_, Aug 01 2025 *) %o A386416 (PARI) apr(n, p, r) = r*binomial(n*p+r, n)/(n*p+r); %o A386416 a(n) = 9^n*apr(n, 8/3, 1/3); %Y A386416 Cf. A004990, A377268, A376636, A004987, A078532, A245114, A008931, A376282. %Y A386416 Cf. A386415. %K A386416 nonn,easy %O A386416 0,2 %A A386416 _Seiichi Manyama_, Jul 21 2025