A189238 E.g.f. x/cos(x)*exp(x/cos(x)).

1, 2, 6, 28, 120, 726, 4424, 31928, 249984, 2131690, 20027392, 199240020, 2162269824, 24676708798, 302660939520, 3897794538864, 53264941301760, 763279034957010, 11499327153704960, 181271619624350860

Offset: 1

Author

Vladimir Kruchinin, Apr 19 2011

Keywords

• nonn

Comments

A(x)=A009843(x)*exp(A009843(x)).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100

Programs

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 */

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.