OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100
FORMULA
a(n)=sum(k=1..n-1, binomial(n,k)*k*(1+(-1)^(n-k))*sum(j=1..m, sum(i=0..floor((j-1)/2), binomial(m,j)/2^(j)*sum((-1)^((n-k)/2-j)*binomial(j,i)*(j-2*i)^(n-k)))*binomial(k+m-1,k-1),m,1,n-k))+n.
PROG
(Maxima)
a(n):=sum(binomial(n, k)*k*(1+(-1)^(n-k))*sum(sum(binomial(m, j)/2^(j)*sum((-1)^((n-k)/2-j)*binomial(j, i)*(j-2*i)^(n-k), i, 0, floor((j-1)/2)), j, 1, m)*binomial(k+m-1, k-1), m, 1, n-k), k, 1, n-1)+n;
(PARI) x='x+O('x^66); /* that many terms */
egf=x/cos(x)*exp(x/cos(x)); /* = x + x^2 + x^3 + 7/6*x^4 + x^5 + 121/120*x^6+ ... */
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 21 2011 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Apr 19 2011
STATUS
approved