cp's OEIS Frontend

E.g.f. A(x) satisfies A(x) = exp( arcsinh(x) * A(x) ).

E.g.f. A(x) satisfies A(x) = ( x + sqrt(x^2 + 1) )^A(x).

a(n) = Sum_{k=0..n} (k+1)^(k-1) * i^(n-k) * A385343(n,k), where i is the imaginary unit.

From Vaclav Kotesovec, Jun 28 2025: (Start)

a(n) ~ 2^n * exp((exp(-1) - 1)*n + 3/2) * n^(n-1) / (sqrt(1 + exp(2*exp(-1))) * (exp(2*exp(-1)) - 1)^(n - 1/2)).

Equivalently, a(n) ~ n^(n-1) / (sqrt(cosh(exp(-1))) * sinh(exp(-1))^(n - 1/2) * exp(n - 3/2)). (End)

E.g.f. A(x) satisfies A(x) = ( (1+x*A(x))/(1-x*A(x)) )^(1/(2*A(x))).

a(n) = Sum_{k=0..n} (n-k+1)^(k-1) * A111594(n,k).

a(n) ~ s * sqrt((-1 + r^2*s^2)/(1 - 2*r^2*(1 + r)*s^2 + r^4*s^4)) * n^(n-1) / (exp(n) * r^(n - 1/2)), where r = 0.4422573061236400123439455590007131605377062990202... and s = 1.93686591146053883124948614770176661449449740697... are the roots of the system of equations ((1 + r*s)/(1 - r*s))^(1/2/s) = s, 2*r*s + (-1 + r^2*s^2)*(log((1 + r*s)/(1 - r*s)) + 2*s) = 0. - Vaclav Kotesovec, Jul 01 2025