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A160537 This is the sequence of integers 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. 1
1, 0, 0, 3, 0, 0, 90, 63, 0, 8880, 22680, 49203, 2118600, 12383280, 60540480, 1131841623, 10857974400, 87893114400, 1246674306240, 15590737021923, 175749917616000, 2471071936993440, 35757593223327360, 502589340005210703 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Appears in the study of the property of the integral Int sin(x)^cos(x) dx. The sequence is increasing of order O((2/pi)^n n!)

LINKS

Table of n, a(n) for n=0..23.

Author?, Int Sin(x)^Cos(x) dx

FORMULA

a(n) = D(sin(x)^cos(x)) (pi/2)

MATHEMATICA

Derivative[n][f][ \[Pi]/2 ]

CROSSREFS

Sequence in context: A037288 A215519 A215679 * A215516 A009133 A180515

Adjacent sequences:  A160534 A160535 A160536 * A160538 A160539 A160540

KEYWORD

nonn

AUTHOR

Ivan (ivantheczar(AT)yahoo.com), May 18 2009

STATUS

approved

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Last modified June 16 12:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)