A296728 - OEIS

%I #11 Dec 19 2017 16:23:52

%S 1,-2,-16,8,12672,571264,-44351360,-12355211520,-452681248768,

%T 478190483394560,132554796040912896,-18854516962334277632,

%U -27186884683859043123200,-5502410397289951851773952,6273206188133923322747420672,5389680791235134726930445369344

%N Expansion of e.g.f. arcsin(x*cos(x)) (odd powers only).

%F a(n) = (2*n+1)! * [x^(2*n+1)] arcsin(x*cos(x)).

%e arcsin(x*cos(x)) = x/1! - 2*x^3/3! - 16*x^5/5! + 8*x^7/7! + 12672*x^9/9! + ...

%t nmax = 16; Table[(CoefficientList[Series[ArcSin[x Cos[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

%o (PARI) first(n) = x='x+O('x^(2*n)); vecextract(Vec(serlaplace(asin(x*cos(x)))), (4^n - 1)/3) \\ _Iain Fox_, Dec 19 2017

%Y Cf. A001818, A009015, A009016, A009446, A009447, A009633, A009634, A012495, A012780, A101928, A191512, A296464, A296466, A296679, A296680, A296729, A296730, A296731, A296740.

%K sign

%O 0,2

%A _Ilya Gutkovskiy_, Dec 19 2017