A381670
The function A(x) = x+(1/2)*x^2-(1/16)*x^4... = Sum_{k >= 0} x^k*A381669(k)/a(k) satisfies the functional equation: x*(A(x)+1) = A(A(x)).
Original entry on oeis.org
1, 1, 2, 1, 16, 16, 64, 16, 1024, 1024, 4096, 2048, 32768, 32768, 131072, 16384, 4194304, 4194304, 16777216, 8388608, 134217728, 134217728, 536870912, 134217728, 8589934592, 8589934592, 34359738368, 17179869184, 274877906944, 274877906944, 1099511627776
Offset: 0
Cf.
A381666 ( A(x)+x = x*A(A(x)) ).
Cf.
A030266 ( A(x)-x = x*A(A(x)) ).
Cf.
A347080 ( A(x)-x = x*A(A(-x)) ).
-
compose(v) = polcoeff(subst(Polrev(v),x,Polrev(v)),#v-1)
optimize(v) = { my(r=1,z = v[#v],t = compose(concat(v,r))); while(t<>z, r = r+(z-t)/2; t = compose(concat(v,r)));concat(v,r) }
listA(max_n) = { my(v=[0, 1], out=[1,1]); while(#v
A381666
The generating function A(x) satisfies the functional equation: A(x)+x = x*A(A(x)).
Original entry on oeis.org
0, -1, 1, 0, -2, 1, 10, -13, -70, 163, 585, -2162, -5361, 30588, 49870, -459125, -411370, 7257651, 1513653, -119997558, 56857538, 2062729507, -2444340720, -36662245639, 71849171621, 670108236318, -1904023701457, -12520858710212, 48731008916451, 237412587011506, -1237341547854760
Offset: 0
G.f.: A(x) = -x + x^2 - 2*x^4 + x^5 + 10*x^6 + ...
A(A(x)) = x - 2*x^3 + x^4 + 10*x^5 - 13*x^6 + ...
Cf.
A030266 ( A(x)-x = x*A(A(x)) ).
Cf.
A347080 ( A(x)-x = x*A(A(-x)) ).
-
a(n) = { my(A=-1+x); for(i=0, n, A=-1+x*A*subst(A, x, x*A+x*O(x^n))); if(n==0,0,polcoeff(A, n-1))}
Showing 1-2 of 2 results.
Comments