cp's OEIS Frontend

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.

A120604 G.f. satisfies: 24*A(x) = 23 + 64*x + A(x)^8, starting with [1,4,28].

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%I A120604 #7 Nov 28 2017 04:04:39
%S A120604 1,4,28,616,15820,453208,13894552,445970128,14796844588,503423385080,
%T A120604 17467725995720,615756709476272,21990183407958584,793912445913712496,
%U A120604 28928560840589374640,1062498482335560005024,39293868860176487815916
%N A120604 G.f. satisfies: 24*A(x) = 23 + 64*x + A(x)^8, starting with [1,4,28].
%C A120604 See comments in A120588 for conditions needed for an integer sequence to satisfy a functional equation of the form: r*A(x) = c + b*x + A(x)^n.
%F A120604 G.f.: A(x) = 1 + Series_Reversion((1+24*x - (1+x)^8)/64). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(8*n,n)/(7*n+1) * (23+64*x)^(7*n+1)/24^(8*n+1). - _Paul D. Hanna_, Jan 24 2008
%F A120604 a(n) ~ 4^(-1 + 3*n) * (-23 + 21*3^(1/7))^(1/2 - n) / (3^(3/7) * n^(3/2) * sqrt(7*Pi)). - _Vaclav Kotesovec_, Nov 28 2017
%e A120604 A(x) = 1 + 4*x + 28*x^2 + 616*x^3 + 15820*x^4 + 453208*x^5 +...
%e A120604 A(x)^8 = 1 + 32*x + 672*x^2 + 14784*x^3 + 379680*x^4 + 10876992*x^5 +...
%t A120604 CoefficientList[1 + InverseSeries[Series[(1+24*x - (1+x)^8)/64, {x, 0, 20}], x], x] (* _Vaclav Kotesovec_, Nov 28 2017 *)
%o A120604 (PARI) {a(n)=local(A=1+4*x+28*x^2+x*O(x^n));for(i=0,n,A=A+(-24*A+23+64*x+A^8)/16);polcoeff(A,n)}
%Y A120604 Cf. A120588 - A120603, A120605 - A120607.
%K A120604 nonn
%O A120604 0,2
%A A120604 _Paul D. Hanna_, Jun 16 2006