A009338 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A009338

Expansion of log(1+sin(x)*cos(x)).

0, 1, -1, -2, 10, -40, 104, 208, -6320, 64640, -436096, 986368, 29459200, -652487680, 8309679104, -60911593472, -294946887680, 20973645824000, -456801564983296, 6185783347314688, -27026064538664960, -1429441147870904320

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) ~ (n-1)! * (-1)^(n+1) * 2^(2*n+1) * cos(n*arctan(2*log(2+sqrt(3))/Pi)) / (Pi^2 + 4*log(2+sqrt(3))^2)^(n/2). - Vaclav Kotesovec, Jan 23 2015

MATHEMATICA

Log[ 1+Sin[ x ]*Cos[ x ] ]

CoefficientList[Series[Log[1 + Cos[x]*Sin[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)

CROSSREFS

Sequence in context: A184433 A339090 A244376 * A261473 A377946 A174395