%I #5 Jan 09 2024 18:45:41
%S 1,1,1,2,6,27,163,1271,12354,145801,2047083,33642256,638588460,
%T 13845027215,339607971556,9347964267192,286688210033698,
%U 9734737020358855,363942977852123850,14906164891970353970,665835978084064725837,32304867226779146102085,1696127595521806495181023
%N G.f. A(x) satisfies: A'(x) = A(B(x)) where B'(x) = A(x) with B(0)=0 and A(0)=1.
%e E.g.f.: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 6*x^4/4! + 27*x^5/5! + 163*x^6/6! +...
%e Related expansions.
%e A'(x) = A(B(x)) = 1 + x + 2*x^2/2! + 6*x^3/3! + 27*x^4/4! + 163*x^5/5! +...
%e where B'(x) = A(x):
%e B(x) = x + x^2/2! + x^3/3! + 2*x^4/4! + 6*x^5/5! + 27*x^6/6! + 163*x^7/7! +...
%o (PARI) {a(n) = my(A=1+x); for(i=1, n, A = 1 + intformal(subst(A, x, intformal(A +x*O(x^n))))); n!*polcoeff(A, n)}
%o for(n=0, 25, print1(a(n), ", "))
%K nonn
%O 0,4
%A _Paul D. Hanna_, Nov 15 2013