A192060 E.g.f. cos(cos(x)-1) (even part).

1, 0, -3, 15, 42, -2895, 54417, -251160, -32268603, 1859064495, -56137896318, -300966155655, 194418466667697, -17000801954550960, 829654990634826717, 8111862191577165855, -7601061861134689474758, 1057729211267718608758065

Offset: 0

Author

Vladimir Kruchinin, Jun 21 2011

Keywords

• sign

Programs

Maxima

a(n):=if n=0 then 1 else 2*(sum(((-1)^(k)*sum(((sum((j-2*i)^(2*n)*binomial(j,i),i,0,(j-1)/2))*binomial(2*k,j)*(-1)^(n-j))/2^j,j,1,2*k))/(2*k)!,k,0,n));

Formula

a(n):=2*(sum(k=0..n, ((-1)^(k)*sum(j=1..2*k, ((sum(i=0..(j-1)/2, (j-2*i)^(2*n)*binomial(j,i)))*binomial(2*k,j)*(-1)^(n-j))/2^j))/(2*k)!)), n>0, a(0)=1.