A160537 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.

1, 0, 0, 3, 0, 0, 90, 63, 0, 8880, 22680, 49203, 2118600, 12383280, 60540480, 1131841623, 10857974400, 87893114400, 1246674306240, 15590737021923, 175749917616000, 2471071936993440, 35757593223327360, 502589340005210703, 7719667979121014400, 124858807502800971600

Offset

0,4

Comments

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!).

Links

Table of n, a(n) for n=0..25.

Author?, Int Sin(x)^Cos(x) dx [broken link]

Formula

a(n) = (d^n/dx^n) (sin(x)^cos(x)) (Pi/2).

Maple

seq(coeftayl(sin(x)^cos(x), x=Pi/2, n)*n!, n=0..25); # Sean A. Irvine, Apr 15 2026

Mathematica

f[x_] := Sin[x]^Cos[x]; a[n_] := Derivative[n][f][Pi/2]; Array[a, 30, 0]

Crossrefs

Sequence in context: A215519 A215679 A215516 * A009133 A180515 A009138

Adjacent sequences: A160534 A160535 A160536 * A160538 A160539 A160540

Keyword

nonn

Author

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

Status

approved