A012821 - OEIS

%I #12 Sep 30 2025 20:34:16

%S 1,1,1,3,9,45,225,1071,6993,56697,467745,3279419,29529753,376156261,

%T 4297350785,35274762407,378759492257,8003761282417,122599030798017,

%U 853554115621363,8002975063348265,450081179390735645

%N Expansion of e.g.f. exp(sec(x)*arcsinh(x)).

%C The first negative number is a(24) = -686072407102337430543.

%H Andrew Howroyd, <a href="/A012821/b012821.txt">Table of n, a(n) for n = 0..200</a>

%e exp(sec(x)*arcsinh(x)) = 1 + x + 1/2!*x^2 + 3/3!*x^3 + 9/4!*x^4 + 45/5!*x^5 + ...

%o (PARI) seq(n)={my(x='x+O('x^n)); Vec(serlaplace(exp(asinh(x)/cos(x))))} \\ _Andrew Howroyd_, Feb 25 2018

%K sign

%O 0,4

%A _Patrick Demichel_