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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
OFFSET
0,3
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
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
Previous Mathematica program replaced by Harvey P. Dale, Dec 09 2021
STATUS
approved