A352252 - OEIS

%I #13 Mar 26 2022 13:41:34

%S 1,1,2,3,0,-55,-480,-3157,-15232,-16623,898560,16316179,194574336,

%T 1666248025,5418649600,-170157839685,-5164467978240,-92955464490463,

%U -1188910801354752,-7329026447550685,157257042777866240,7516793832172469481,187200588993188069376

%N Expansion of e.g.f. 1 / (1 - x * cos(x)).

%H Seiichi Manyama, <a href="/A352252/b352252.txt">Table of n, a(n) for n = 0..456</a>

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n,2*k+1) * (2*k+1) * a(n-2*k-1).

%t nmax = 22; CoefficientList[Series[1/(1 - x Cos[x]), {x, 0, nmax}], x] Range[0, nmax]!

%t a[0] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n, 2 k + 1] (2 k + 1) a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 22}]

%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(1 / (1 - x * cos(x)))) \\ _Michel Marcus_, Mar 10 2022

%Y Cf. A000111, A007289, A009189, A094088, A205571, A302397, A352250, A352251.

%K sign

%O 0,3

%A _Ilya Gutkovskiy_, Mar 09 2022