OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..250
FORMULA
a(n) = (n-1)!*Sum_{k=1..n} (k-1)!*a(n-k)/(n-k)! for n > 0 with a(0)=1.
a(n) ~ (n-1)!^2. - Vaclav Kotesovec, Jul 10 2018
EXAMPLE
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 8*x^3/3! + 62*x^4/4! + 862*x^5/5! + ...
log(A(x)) = x + x^2/2 + 2!*x^3/3 + 3!*x^4/4 + 4!*x^5/5 + 5!*x^6/6 + ...
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-i)*binomial(n-1, i-1)*(i-1)!^2, i=1..n))
end:
seq(a(n), n=0..20); # Alois P. Heinz, Aug 13 2019
MATHEMATICA
a:= CoefficientList[Series[Exp[Sum[(n - 1)!*x^n/n, {n, 1, 500}]], {x, 0, 35}], x]; Table[a[[n]]*(n - 1)!, {n, 1, 30}] (* G. C. Greubel, Jul 09 2018 *)
PROG
(PARI) {a(n)=n!*polcoeff(exp(sum(k=1, n, (k-1)!*x^k/k)+x*O(x^n)), n)}
(PARI) {a(n)=if(n==0, 1, (n-1)!*sum(k=1, n, (k-1)!*a(n-k)/(n-k)!))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 15 2009
STATUS
approved