|
%I #6 Jan 27 2020 21:50:44
%S 1,-1,-2,-1,253,12854,668053,39148199,2456262898,130790155859,
%T -3853032641387,-4312625669814166,-1531200886955161127,
%U -489884373969089299201,-159097972223555719000922,-54064488830901650420384521,-19284261543086608770504566147
%N E.g.f.: exp(1 - sec(x)) (even powers only).
%F a(0) = 1; a(n) = -Sum_{k=1..n} binomial(2*n-1,2*k-1) * A000364(k) * a(n-k).
%t nmax = 16; Table[(CoefficientList[Series[Exp[1 - Sec[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%t a[0] = 1; a[n_] := a[n] = -Sum[Binomial[2 n - 1, 2 k - 1] Abs[EulerE[2 k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]
%o (PARI) a(n) = {polcoef(serlaplace(exp(1 - 1/cos(x + O(x^(2*n + 1))))), 2*n)} \\ _Andrew Howroyd_, Jan 27 2020
%Y Cf. A000364, A005046, A217502, A260884.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Jan 27 2020
|
