cp's OEIS Frontend

A307366 G.f. A(x) satisfies: A(x) = x*exp(A(-x) - A(-x^2)/2 + A(-x^3)/3 - A(-x^4)/4 + ...).

%I A307366 #5 Apr 05 2019 17:46:28
%S A307366 0,1,-1,0,0,1,-2,-1,3,3,-8,-5,17,15,-47,-35,118,91,-311,-240,839,660,
%T A307366 -2314,-1809,6417,5035,-18002,-14177,51016,40322,-145784,-115402,
%U A307366 419197,332457,-1212617,-963586,3526976,2807301,-10307097,-8215194,30246994,24139050,-89101081
%N A307366 G.f. A(x) satisfies: A(x) = x*exp(A(-x) - A(-x^2)/2 + A(-x^3)/3 - A(-x^4)/4 + ...).
%F A307366 G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} (1 + x^n)^((-1)^n*a(n)).
%F A307366 Recurrence: a(n+1) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+d+1)*d*a(d) ) * a(n-k+1).
%e A307366 G.f.: A(x) = x - x^2 + x^5 - 2*x^6 - x^7 + 3*x^8 + 3*x^9 - 8*x^10 - 5*x^11 + 17*x^12 + ...
%t A307366 terms = 42; A[_] = 0; Do[A[x_] = x Exp[Sum[(-1)^(k + 1) A[-x^k]/k, {k, 1, terms}]] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
%t A307366 a[n_] := a[n] = SeriesCoefficient[x Product[(1 + x^k)^((-1)^k a[k]), {k, 1, n - 1}], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 0, 42}]
%Y A307366 Cf. A000081, A004111, A045648, A049075, A307365.
%K A307366 sign
%O A307366 0,7
%A A307366 _Ilya Gutkovskiy_, Apr 05 2019