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

0,3

Links

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

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

Example

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

Prog

(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)

Crossrefs

Cf. A096542.

Sequence in context: A196125 A345103 A367385 * A115047 A000364 A028296

Adjacent sequences: A096534 A096535 A096536 * A096538 A096539 A096540

Keyword

nonn

Author

Paul D. Hanna, Jun 24 2004

Status

approved