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%I #11 Mar 01 2022 11:59:34
%S 1,-1,1,-1,1,-1,2,-3,4,-5,6,-8,11,-15,20,-26,34,-45,60,-80,106,-140,
%T 185,-245,325,-431,571,-756,1001,-1326,1757,-2329,3086,-4088,5415,
%U -7173,9504,-12593,16685,-22105,29284,-38796,51400,-68100,90225,-119535,158365,-209810,277970,-368275,487916,-646421,856416
%N G.f. satisfies: A(x) = 1/(1 + x*A(x^5)) and also the continued fraction: 1+x*A(x^6) = [1;1/x,1/x^5,1/x^25,1/x^125,...,1/x^(5^(n-1)),...].
%F a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/5)} a(k) * a(n-5*k-1). - _Ilya Gutkovskiy_, Mar 01 2022
%o (PARI) a(n)=local(A);A=1-x;for(i=1,n\5+1, A=1/(1+x*subst(A,x,x^5)+x*O(x^n)));polcoeff(A,n,x)
%o (PARI) a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(5))+1,n,1/x^(5^(n-1)))))); polcoeff(M[1,1]/M[2,1]+x*O(x^(6*n+1)),6*n+1)
%Y Cf. A101912, A101913, A101914, A101916, A101917, A101918.
%K sign
%O 0,7
%A _Paul D. Hanna_, Dec 20 2004
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