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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 7 02:20 EST 2023. Contains 367622 sequences. (Running on oeis4.)