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.

A118792 E.g.f.: -log(1 - (1 - sqrt(5 - 4*exp(x)) )/2 ).

This page as a plain text file.
%I A118792 #9 Jun 13 2015 17:40:46
%S A118792 0,1,4,30,352,5670,116344,2902830,85326112,2887962870,110620824904,
%T A118792 4730842053630,223445584599472,11552029520192070,648869447924011864,
%U A118792 39347855472366932430,2562065820090343738432,178286102174571726213270
%N A118792 E.g.f.: -log(1 - (1 - sqrt(5 - 4*exp(x)) )/2 ).
%C A118792 Also equals the unsigned row sums of triangle A118791 (offset without leading zero).
%F A118792 a(n) = (n-1)!*Sum_{k=0..n-1} abs( [x^k] (x/log(1-x-x^2))^n ) for n>0.
%F A118792 a(n) ~ sqrt(5/2)*n^(n-1)/(exp(n)*(log(5/4))^(n-1/2)). - _Vaclav Kotesovec_, Jun 26 2013
%e A118792 E.g.f.: A(x) = x + 2*x^2 + 30/6*x^3 + 352/24*x^4 + 5670/120*x^5 +...
%t A118792 CoefficientList[Series[-Log[1-(1-Sqrt[5-4*Exp[x]])/2], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 26 2013 *)
%o A118792 (PARI) a(n)=local(x=X+X^2*O(X^n));n!*polcoeff(-log(1-(1-sqrt(5-4*exp(x)))/2),n,X)
%o A118792 (PARI) /* As the unsigned row sums of A118791: */ a(n)=local(x=X+X^2*O(X^n));if(n<1,0, (n-1)!*sum(k=0,n-1,abs(polcoeff(((-x/log(1-x-x^2)))^n,k,X))))
%Y A118792 Cf. A118791.
%K A118792 nonn
%O A118792 0,3
%A A118792 _Paul D. Hanna_, Apr 30 2006