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%I A326553 #3 Jul 26 2019 22:08:49
%S A326553 1,3,19,189,2521,41813,826099,18889209,489450841,14142037665,
%T A326553 449838952795,15587619260117,583210749984409,23380025164256829,
%U A326553 997331252199242083,44981225190596283921,2131771651553974931929,105498794931132306727769,5415121471957856287745611,286003536194104676920620909,15383978962252356122447259865
%N A326553 E.g.f. A(x) satisfies: Sum_{n>=1} (-1)^(n-1) * A(x)^n / (n + A(x)^n) = x.
%F A326553 E.g.f.: Series_Reversion( Sum_{n>=1} (-1)^(n-1) * x^n / (n + x^n) ).
%e A326553 E.g.f.: A(x) = x + 3*x^2/2! + 19*x^3/3! + 189*x^4/4! + 2521*x^5/5! + 41813*x^6/6! + 826099*x^7/7! + 18889209*x^8/8! + 489450841*x^9/9! + 14142037665*x^10/10! + 449838952795*x^11/11! + ...
%e A326553 such that
%e A326553 x = A(x)/(1 + A(x)) + A(x)^2/(2 + A(x)^2) + A(x)^3/(3 + A(x)^3) + A(x)^4/(4 + A(x)^4) + A(x)^5/(5 + A(x)^5) + A(x)^6/(6 + A(x)^6) + ...
%e A326553 The series reversion of the e.g.f. begins:
%e A326553 Series_Reversion(A(x)) = x - 3*x^2/2! + 8*x^3/3! - 24*x^4/4! + 144*x^5/5! - 1010*x^6/6! + 5760*x^7/7! - 40320*x^8/8! + 416640*x^9/9! - 4250232*x^10/10! + 43545600*x^11/11! - 511526400*x^12/12! + ...
%e A326553 which equals Sum_{n>=1} (-1)^(n-1) * x^n / (n + x^n).
%o A326553 (PARI) {a(n) = my(A = serreverse( sum(m=1,n+1, (-1)^(m-1)*x^m/(m + x^m +x*O(x^n))) ));
%o A326553 n!*polcoeff(H=A,n)}
%o A326553 for(n=1,25,print1(a(n),", "))
%K A326553 nonn
%O A326553 1,2
%A A326553 _Paul D. Hanna_, Jul 26 2019

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