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
Keywords
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
Programs
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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