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

0,3

Links

Table of n, a(n) for n=0..17.

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.

Prog

(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));

Crossrefs

Sequence in context: A346142 A366576 A093627 * A316642 A146805 A147057

Adjacent sequences: A192057 A192058 A192059 * A192061 A192062 A192063

Keyword

sign

Author

Vladimir Kruchinin, Jun 21 2011

Status

approved