This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341957 #7 Mar 10 2021 11:30:13
%S A341957 1,1,8,144,4554,230940,18177900,2196712980,406693854000,
%T A341957 115319921466960,50017977456121080,33099984846144881280,
%U A341957 33309128229289401091680,50790831819884758635873840,116936359809482874588941613600,405126119455062475269210516705600
%N A341957 E.g.f. A(x) satisfies: Sum_{n>=0} A(x)^n * exp(2^n*A(x)) / n! = Sum_{n>=0} x^n/(1 - 2^n*x).
%e A341957 E.g.f.: A(x) = x + x^2/2! + 8*x^3/3! + 144*x^4/4! + 4554*x^5/5! + 230940*x^6/6! + 18177900*x^7/7! + 2196712980*x^8/8! + 406693854000*x^9/9! + 115319921466960*x^10/10! + ...
%e A341957 such that
%e A341957 Sum_{n>=0} A(x)^n * exp(2^n*A(x)) / n! = exp(A(x)) + A(x)*exp(2*A(x)) + A(x)^2*exp(2^2*A(x))/2! + A(x)^3*exp(2^3*A(x))/3! + A(x)^4*exp(2^4*A(x))/4! +...
%e A341957 equals the sum
%e A341957 Sum_{n>=0} x^n/(1 - 2^n*x) = 1 + 2*x + 4*x^2 + 10*x^3 + 34*x^4 + 162*x^5 + 1090*x^6 + 10370*x^7 + 139522*x^8 + ... + A117402(n)*x^n + ...
%e A341957 RELATED SERIES.
%e A341957 exp(A(x)) = 1 + x + 2*x^2/2! + 12*x^3/3! + 186*x^4/4! + 5460*x^5/5! + 263940*x^6/6! + 20053740*x^7/7! + 2359326480*x^8/8! + 428122913400*x^9/9! + ...
%o A341957 (PARI) {a(n) = my(L=[0,1]); for(i=1,n, L=concat(L,0);
%o A341957 L[#L] = polcoeff( sum(n=0,#L, x^n/(1 - 2^n*x +x*O(x^#L))) - sum(n=0,#L, Ser(L)^n/n! * exp(2^n*Ser(L)) ) ,#L-1)/2;); n!*L[n+1]}
%o A341957 for(n=1,20,print1(a(n),", "))
%Y A341957 Cf. A117402.
%K A341957 nonn
%O A341957 1,3
%A A341957 _Paul D. Hanna_, Mar 09 2021