OFFSET
0,4
LINKS
Robert Israel, Table of n, a(n) for n = 0..449
FORMULA
a(n) ~ n! * (-1)^(n+1) * sin(1) / 2. - Vaclav Kotesovec, Jan 23 2015
From Robert Israel, Jan 07 2019: (Start)
E.g.f.: sin(x)*(1+x+1/(1+x))/2.
a(2*k) = (-1)^(k+1)*k - (2*k)!*Sum_{j=0..k-1} (-1)^j/(2*(2*j+1)!).
a(2*k+1) = (-1)^k + (2*k+1)!*Sum_{j=0..k-1} (-1)^j/(2*(2*j+1)!).
(End)
MAPLE
S:= series(sin(x)*(1+x+1/(1+x))/2, x, 51):
seq(coeff(S, x, j)*j!, j=0..50); # Robert Israel, Jan 07 2019
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Sin[x]*Cosh[Log[1+x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 20 2015 *)
CoefficientList[Series[((1 + (1 + x)^2)*Sin[x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
Prior Mathematica program replaced by Harvey P. Dale, Aug 20 2015
STATUS
approved