A159476 Expansion of e.g.f.: A(x) = exp( Sum_{n>=1} (n-1)!*x^n/n ).

1, 1, 2, 8, 62, 862, 19492, 656224, 30739676, 1906807004, 151002453464, 14846381034784, 1772922018732328, 252631570039665832, 42329528274029082608, 8237406877267427867648, 1842215469973381977889808, 469160036709398319115207696, 134976328490030629922214893344

Offset: 0

Author

Paul D. Hanna, Apr 15 2009

Keywords

• nonn

Examples

			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 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A158876, A293847.

Programs

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 *)

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)!))}

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