%I #20 Sep 17 2025 08:53:08

%S 1,1,0,-3,4,50,-264,-1638,25264,40896,-3357360,13380840,559239264,

%T -7126367664,-98536058880,3137828374800,8293939695360,

%U -1427422903584000,10789876955529216,666226173751955712,-14427332604300810240,-279534553922071445760

%N The exponential generating function A(x) = Sum a(j) x^j/j! satisfies the functional equation A(x)=1+x*(A(x))*(1-log(A(x))).

%F a(n) = (n-1)! * Sum_{i=0..n-1} (binomial(n,i) * Sum_{j=0..n} (-1)^j * j! * binomial(n,j) * stirling1(n-i-1,j)) / (n-i-1)!, n>0, a(0)=1. [_Vladimir Kruchinin_, Oct 13 2012]

%o (Maxima)

%o a(n):=if n=0 then 1 else ((n-1)!*sum((binomial(n,i)*sum(j!*(-1)^(j)*binomial(n,j)*stirling1(n-i-1,j),j,0,n))/(n-i-1)!,i,0,n-1)); /* _Vladimir Kruchinin_, Oct 13 2012 */

%K easy,sign

%O 0,4

%A Jim Ferry (jferry(AT)alum.mit.edu), Mar 14 2003

%E Entry revised by _Vladimir Kruchinin_, Oct 13 2012

%E Further edited by _N. J. A. Sloane_, Jan 19 2019 following advice from Gilbert Labelle.