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 A131927 #32 May 21 2025 06:34:08
%S A131927 0,1,8,136,2888,68680,1749896,46707976,1289214152,36496595656,
%T A131927 1053849164552,30918300671368,919029058099784,27617782977715528,
%U A131927 837674888992142984,25610757376777402888,788450850824647610312
%N A131927 Expansion of series reversion of x * (1 - 9*x) / (1 - x).
%C A131927 The Hankel transform of this sequence is 72^C(n+1,2).
%H A131927 G. C. Greubel, <a href="/A131927/b131927.txt">Table of n, a(n) for n = 0..650</a>
%F A131927 a(n) = Sum_{k=0..n} A086810(n,k)*8^k.
%F A131927 G.f.: (1+x-sqrt(1-34*x+x^2))/18. - _Emeric Deutsch_, Nov 19 2007
%F A131927 a(n) = - a(n-1) + 9 * Sum_{k=1..n-1} a(k) * a(n-k) if n>1. - _Michael Somos_, Jul 23 2011
%F A131927 Recurrence: n*a(n) = 17*(2*n-3)*a(n-1) - (n-3)*a(n-2). - _Vaclav Kotesovec_, Aug 20 2013
%F A131927 a(n) ~ sqrt(102*sqrt(2)-144) * (17+12*sqrt(2))^n/(18*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Aug 20 2013
%F A131927 0 = +a(n)*(+a(n+1) - 85*a(n+2) + 4*a(n+3)) + a(n+1)*(+17*a(n+1) + 1154*a(n+2) - 85*a(n+3)) + a(n+2)*(+17*a(n+2) + a(n+3)) for all n>0. - _Michael Somos_, Aug 30 2014
%F A131927 G.f.: x/(1 - 8*x/(1 - 9*x/(1 - 8*x/(1 - 9*x/(1 - 8*x/(1 - ...)))))), a continued fraction. - _Ilya Gutkovskiy_, Apr 21 2017
%e A131927 G.f. = x + 8*x^2 + 136*x^3 + 2888*x^4 + 68680*x^5 + 1749896*x^6 + 46707976*x^7 + ...
%p A131927 G:=(1+x-sqrt(1-34*x+x^2))*1/18: Gser:=series(G,x=0,21): seq(coeff(Gser,x,n), n =0..17) # _Emeric Deutsch_, Nov 19 2007
%t A131927 CoefficientList[InverseSeries[Series[x*(1-9*x)/(1-x),{x,0,20}],x],x] (* _Vaclav Kotesovec_, Aug 20 2013 *)
%t A131927 a[ n_] := SeriesCoefficient[ (1 + x - Sqrt[ 1 - 34 x + x^2]) / 18, {x, 0, n}]; (* _Michael Somos_, Aug 30 2014 *)
%t A131927 a[ n_] := If[ n < 1, 0, SeriesCoefficient[ InverseSeries[ Series[ x (1 - 9 x) / (1 - x), {x, 0, n}]], {x, 0, n}]]; (* _Michael Somos_, Aug 30 2014 *)
%o A131927 (PARI) {a(n) = local(A); if( n<1, 0, A = vector(n); A[1] = 1;for( k=2, n, A[k] = - A[k-1] + 9 * sum( j=1, k-1, A[j] * A[k-j])); A[n])}; /* _Michael Somos_, Jul 23 2011 */
%K A131927 nonn
%O A131927 0,3
%A A131927 _Philippe Deléham_, Oct 29 2007
%E A131927 More terms from _Emeric Deutsch_, Nov 19 2007