A304637 - OEIS

%I #4 May 15 2018 17:37:16

%S 1,1,2,19,299,6241,160020,4858616,171069361,6885389368,313162056098,

%T 15930678907603,897891292501468,55589209442827830,3751221859059876602,

%U 274034654053985700103,21542764404180713248407,1813058710831887654110832,162622164570756746546500432,15484376910535107858657060827,1559723646248351386009584065673,165693824812298090074580795882273

%N G.f. A(x) satisfies: A(x) = 1 + x*Sum_{n>=0} (A(x)^n - 1/A(x)^n)^n.

%e G.f.: A(x) = 1 + x + 2*x^2 + 19*x^3 + 299*x^4 + 6241*x^5 + 160020*x^6 + 4858616*x^7 + 171069361*x^8 + 6885389368*x^9 + 313162056098*x^10 + ...

%e such that g.f. A = A(x) satisfies:

%e A(x) = 1 + x*(1 + (A - 1/A) + (A^2 - 1/A^2)^2 + (A^3 - 1/A^3)^3 + (A^4 - 1/A^4)^4 + (A^5 - 1/A^5)^5 + ...).

%e RELATED SERIES.

%e x/Series_Reversion(A(x) - 1) = 1 + 2*x + 15*x^2 + 201*x^3 + 3807*x^4 + 93103*x^5 + 2788528*x^6 + 98816388*x^7 + 4043274742*x^8 + 187583369889*x^9 + 9729671519992*x^10 + ...

%o (PARI) {a(n) = my(A=1); for(i=1,n, A = 1 + x*sum(m=0,n, (A^m - 1/A^m +x*O(x^n))^m )); polcoeff(A,n)}

%o for(n=0,30,print1(a(n),", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 15 2018