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A160537
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a(n) = n!*c(n) where c(n) is the coefficient of the Taylor power series expansion of the real function sin(x)^cos(x) defined on (0,Pi), expanded around the point x = Pi/2.
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1
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1, 0, 0, 3, 0, 0, 90, 63, 0, 8880, 22680, 49203, 2118600, 12383280, 60540480, 1131841623, 10857974400, 87893114400, 1246674306240, 15590737021923, 175749917616000, 2471071936993440, 35757593223327360, 502589340005210703
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OFFSET
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0,4
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COMMENTS
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Appears in the study of the property of the integral Integral sin(x)^cos(x) dx.
The sequence is increasing of order O((2/Pi)^n n!).
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LINKS
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FORMULA
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a(n) = D(sin(x)^cos(x)) (Pi/2).
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MATHEMATICA
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Derivative[n][f][ \[Pi]/2 ]
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CROSSREFS
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KEYWORD
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nonn,uned
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AUTHOR
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Ivan (ivantheczar(AT)yahoo.com), May 18 2009
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STATUS
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approved
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