A352121 - OEIS

%I #15 Mar 06 2022 08:40:58

%S 1,1,-3,13,-87,841,-10683,167413,-3113967,66991441,-1635760563,

%T 44683635613,-1350018280647,44694643670041,-1608962582321643,

%U 62572776778020613,-2614314267900284127,116781203402752052641,-5553985490569476301923

%N Expansion of e.g.f. sqrt(2 - exp(-2*x)).

%F a(n) = Sum_{k=0..n} (-2)^(n-k) * (Product_{j=0..k-1} (-2*j+1)) * Stirling2(n,k).

%F a(n) ~ (-1)^(n+1) * 2^n * n^(n-1) / (log(2)^(n - 1/2) * exp(n)). - _Vaclav Kotesovec_, Mar 06 2022

%t m = 18; Range[0, m]! * CoefficientList[Series[(2 - Exp[-2*x])^(1/2), {x, 0, m}], x] (* _Amiram Eldar_, Mar 05 2022 *)

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sqrt(2-exp(-2*x))))

%o (PARI) a(n) = sum(k=0, n, (-2)^(n-k)*prod(j=0, k-1, -2*j+1)*stirling(n, k, 2));

%Y Cf. A352122, A352123.

%Y Cf. A352075.

%K sign

%O 0,3

%A _Seiichi Manyama_, Mar 05 2022