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 A009541 Expansion of sin(x)*exp(sin(x)). 1
 0, 1, 2, 2, -4, -24, -42, 104, 888, 1792, -8086, -68608, -115468, 1203840, 8863806, 5570816, -275344656, -1636425728, 2488177106, 86205304832, 369676840940, -2289265803264, -34139482063962, -73881736609792, 1691837365047912 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..24. FORMULA a(n)=sum(k=1..n, (1+(-1)^(n-k))*2^(-k)*sum(i=0..k/2, (-1)^((n+k)/2-i)*binomial(k,i)*(2*i-k)^n)/(k-1)!). - Vladimir Kruchinin, Apr 19 2011 a(n) = D^n(x*exp(x)) evaluated at x = 0, where D is the operator sqrt(1-x^2)*d/dx. Cf. A009623. - Peter Bala, Dec 06 2011 MATHEMATICA With[{nn=30}, CoefficientList[Series[Sin[x]*Exp[Sin[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 09 2021 *) PROG (Maxima) a(n):=sum((1+(-1)^(n-k))*2^(-k)*sum((-1)^((n+k)/2-i)*binomial(k, i)*(2*i-k)^n, i, 0, k/2)/(k-1)!, k, 1, n); /* Vladimir Kruchinin, Apr 19 2011 */ CROSSREFS A009623. Sequence in context: A270527 A232275 A257612 * A307969 A212672 A362766 Adjacent sequences: A009538 A009539 A009540 * A009542 A009543 A009544 KEYWORD sign,easy AUTHOR R. H. Hardin EXTENSIONS Extended with signs by Olivier Gérard, Mar 15 1997 Previous Mathematica program replaced by Harvey P. Dale, Dec 09 2021 STATUS approved

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Last modified September 13 00:40 EDT 2024. Contains 375857 sequences. (Running on oeis4.)