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A237655 G.f.: exp( Sum_{n>=1} 5*Fibonacci(n-2)*Fibonacci(n+2) * x^n/n ).

%I A237655 #22 Jul 01 2023 14:15:02
%S A237655 1,10,50,175,510,1376,3625,9500,24875,65125,170500,446375,1168625,
%T A237655 3059500,8009875,20970125,54900500,143731375,376293625,985149500,
%U A237655 2579154875,6752315125,17677790500,46281056375,121165378625,317215079500,830479859875,2174224500125,5692193640500,14902356421375,39014875623625
%N A237655 G.f.: exp( Sum_{n>=1} 5*Fibonacci(n-2)*Fibonacci(n+2) * x^n/n ).
%C A237655 Given g.f. A(x), note that A(x)^(1/5) is not an integer series.
%H A237655 Fung Lam, <a href="/A237655/b237655.txt">Table of n, a(n) for n = 0..2000</a>
%H A237655 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3, -1).
%F A237655 G.f.: (1+x)^7 / (1-3*x+x^2).
%F A237655 a(n) = 3*a(n-1) - a(n-2), n>=8. - _Fung Lam_, May 19 2014
%e A237655 G.f.: A(x) = 1 + 10*x + 50*x^2 + 175*x^3 + 510*x^4 + 1376*x^5 + 3625*x^6 + ...
%e A237655 where the logarithm begins:
%e A237655 log(A(x)) = 5*1*2*x + 5*0*3*x^2/2 + 5*1*5*x^3/3 + 5*1*8*x^4/4 + 5*2*13*x^5/5 + 5*3*21*x^6/6 + 5*5*34*x^7/7 + 5*8*55*x^8/8 + 5*13*89*x^9/9 + ...
%o A237655 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, 5*fibonacci(m-2)*fibonacci(m+2) *x^m/m) +x*O(x^n)), n)}
%o A237655 for(n=0,30,print1(a(n),", "))
%Y A237655 Cf. A237654, A054888.
%K A237655 nonn
%O A237655 0,2
%A A237655 _Paul D. Hanna_, May 05 2014