A096537 E.g.f.: A(x) = exp(x*exp(2*x*exp(3*x*exp(...exp(n*x*exp(...))...)))), for n>=1.

1, 1, 5, 61, 1377, 49721, 2625313, 190735749, 18246616321, 2223115264945, 336071395603521, 61725395919953789, 13537971184957280449, 3494778862390292571849, 1048886507411306132337889

Offset: 0

Author

Paul D. Hanna, Jun 24 2004

Keywords

• nonn

Examples

			A(x) = 1 + 1*x + 5*x^2/2! + 61*x^3/3! + 1377*x^4/4! + 49721*x^5/5! +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A096542.

Programs

PARI

a(n)=local(A=exp(x));for(i=1,n,A=exp(x*(n-i+1)*A+x*O(x^n)));n!*polcoeff(A,n)

Formula

Row sums of triangle A096542; also a(n) = A096542(n+1, 1)/(n+1) for n>=0.

Conjecture: a(n) ~ 2 * Pi * n^(2*n + 1/2) / (exp(n) * (exp(1) - 1)^n). - Vaclav Kotesovec, Dec 16 2019