OFFSET
1,2
FORMULA
a(n) = n!*T(n,1), T(n,m) = sum(k=1..n-m, T(n-m,k)*m^k/k! - (2^(-m-k+1)*sum(i=0..m+k-1,(m+k-2*i-1)^(n-m-k+1)*binomial(m+k-1,i),i,0,m+k-1))/(n-m-k+1)!*T(k+m-1,m)), n>m, with T(n,n)=1.
PROG
(Maxima)
array(B, 100, 100);
fillarray (B, makelist (-1, i, 1, 10000));
T(n, m):=if B[n, m]=-1 then B[n, m]:(if n=m then 1 else sum(T(n-m, k)*m^k/k!-(2^(-m-k+1)*sum((m+k-2*i-1)^(n-m-k+1)*binomial(m+k-1, i), i, 0, m+k-1))/(n-m-k+1)!*T(k+m-1, m), k, 1, n-m)) else B[n, m];
makelist(n!*T(n, 1), n, 1, 27);
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Dec 06 2011
STATUS
approved