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))).

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

Links

Table of n, a(n) for n=0..21.

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

Adjacent sequences: A080070 A080071 A080072 * A080074 A080075 A080076

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