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A009343 Expansion of e.g.f. log(1+sin(x)/exp(x)). 0
0, 1, -3, 10, -50, 340, -2888, 29440, -350160, 4759760, -72787488, 1236761920, -23115758720, 471323145280, -10410977045888, 247656022739200, -6312036805140480, 171600628707334400, -4956751714926617088 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved

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Last modified June 24 02:53 EDT 2024. Contains 373661 sequences. (Running on oeis4.)