login
A080073
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))).
0
1, 1, 0, -3, 4, 50, -264, -1638, 25264, 40896, -3357360, 13380840, 559239264, -7126367664, -98536058880, 3137828374800, 8293939695360, -1427422903584000, 10789876955529216, 666226173751955712, -14427332604300810240, -279534553922071445760
OFFSET
0,4
FORMULA
It follows that:
a(n)=((n-1)!*sum(i=0..n-1, (binomial(n,i)*sum(j=0..n, j!*(-1)^(j)*binomial(n,j)*stirling1(n-i-1,j)))/(n-i-1)!)), n>0, a(0)=1. [Vladimir Kruchinin, Oct 13 2012]
PROG
(Maxima)
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]
CROSSREFS
Sequence in context: A032839 A056855 A208653 * A032840 A114694 A272337
KEYWORD
easy,sign
AUTHOR
Jim Ferry (jferry(AT)alum.mit.edu), Mar 14 2003
EXTENSIONS
Entry revised by Vladimir Kruchinin, Oct 13 2012
Further edited by N. J. A. Sloane, Jan 19 2019 following advice from Gilbert Labelle.
STATUS
approved