OFFSET
1,2
COMMENTS
See A005493 for references and links.
FORMULA
a(1) = 1 * SUM(i=0 to 0)combination(1,i) = 1, a(2) = 2 * SUM(i=0 to 1)combination(2,i) = 6, a(n) = n![SUM(i=2 to n-1) combination(n,i) * {SUM(j=1 to i-1) * a(j)/j! } + SUM(i=0 to n-1) combination(n,i)], for n > 2.
EXAMPLE
a(1) = 1 * SUM(i=0 to 0)combination(1,i) = 1,
a(2) = 2 * SUM(i=0 to 1)combination(2,i) = 6,
a(3) = 3![combination(3,2) * a(1)/1! + combination(3,2) + combination(3,1) + combination(3,0)] = 60,
a(4) = 4![combination(4,3) * {a(2)/2! + a(1)/1!} + combination(4,2) * a(1)/1! + combination(4,3) + combination(4,2) + combination(4,1) + combination(4,0)] = 888,
a(5) = 5![combination(5,4) * {a(3)/3! + a(2)/2! + a(1)/1!} + combination(5,3) * {a(2)/2! + a(1)/1!} + combination(5,2) * a(1)/1! + combination(5,4) + combination(5,3) + combination(5,2) + combination(5,1) + combination(5,0)] = 18120.
CROSSREFS
KEYWORD
nonn
AUTHOR
David Yeung (wkyeung(AT)hkbu.edu.hk), May 08 2008
STATUS
approved