OFFSET
1,4
PROG
(Maxima)
Composita(n, k, F):=block([], if k=1 then F(n) else if n=k then (F(1))^n else sum(F(i+1)*Composita(n-i-1, k-1, F), i, 0, n-k));
SolveDiff21(G, key):=block([b], array(b, 100), b[1]:1, b[2]:1/2, bfun(n):=b[n], makelist(b[n]:-b[n-1]/n+1/(n*(n-1))*sum(Composita(n-2, k, bfun)*G(k) , k, 1, n-2), n, 3, 20),
if key=1 then makelist(n!*b[n], n, 1, 20) else makelist(b[n], n, 1, 20));
f(n):=1/n!;
SolveDiff21(f, 1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Nov 25 2011
STATUS
approved