A009442 E.g.f. log(1 + x/cos(x)).

0, 1, -1, 5, -18, 109, -720, 5977, -56336, 612729, -7453440, 100954061, -1502172672, 24395453861, -429076910080, 8128143367905, -164961704478720, 3571195811862385, -82142328351817728, 2000535014776893973

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n)=2*n!*sum(m=1..(n-1)/2, ((-1)^(n-1)*sum(j=0..m, binomial((n/2-m+j-1),j)*4^(m-j)*sum(i=0..j, (i-j)^(2*m)*binomial(2*j,i)*(-1)^(m+j-i))))/((n-2*m)*(2*m)!))+(-1)^(n-1)*n!/n. - Vladimir Kruchinin, Jun 16 2011

a(n) ~ (n-1)! * (-1)^(n+1) / r^n, where r = 0.7390851332151606416553120876738734040134117589... (see A003957) is the root of the equation cos(r) = r. - Vaclav Kotesovec, Jan 24 2015

Mathematica

CoefficientList[Series[Log[1 + x*Sec[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

Prog

(Maxima)
a(n):=2*n!*sum(((-1)^(n-1)*sum(binomial((n/2-m+j-1), j)*4^(m-j)*sum((i-j)^(2*m)*binomial(2*j, i)*(-1)^(m+j-i), i, 0, j), j, 0, m))/((n-2*m)*(2*m)!), m, 1, (n-1)/2)+(-1)^(n-1)*n!/n; /* Vladimir Kruchinin, Jun 16 2011 */

Crossrefs

Cf. A003957.

Sequence in context: A127756 A228614 A158455 * A332784 A302435 A332467

Adjacent sequences: A009439 A009440 A009441 * A009443 A009444 A009445

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved