A009343 Expansion of e.g.f. log(1+sin(x)/exp(x)).

0, 1, -3, 10, -50, 340, -2888, 29440, -350160, 4759760, -72787488, 1236761920, -23115758720, 471323145280, -10410977045888, 247656022739200, -6312036805140480, 171600628707334400, -4956751714926617088

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: log(1+sin(x)/exp(x)).

a(n) = 2*Sum_(k=1..n, Sum_(j=0..(n-k)/2, C(n,n-k-2*j)*(k^(n-k-2*j) *Sum_(i=0..k/2, (2*i-k)^(k+2*j)*C(k,i)*(-1)^(k+j-i))))/(2^k*k)). - Vladimir Kruchinin, Jun 13 2011

a(n) ~ (-1)^(n+1) * (n-1)! / r^n, where r = 0.588532743981861... is the real root of the equation sin(r) = exp(-r). - Vaclav Kotesovec, Oct 25 2013

Mathematica

CoefficientList[Series[Log[1+Sin[x]/Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 25 2013 *)

Prog

(Maxima)
a(n):=2*sum(sum(binomial(n, n-k-2*j)*(k^(n-k-2*j)*sum((2*i-k)^(k+2*j) *binomial(k, i)*(-1)^(k+j-i), i, 0, k/2)), j, 0, (n-k)/2)/(2^k*k), k, 1, n); [Vladimir Kruchinin, Jun 13 2011]

Crossrefs

Sequence in context: A276028 A209902 A049370 * A352414 A341648 A307099

Adjacent sequences: A009340 A009341 A009342 * A009344 A009345 A009346

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved