A354546 - OEIS

%I #16 Aug 18 2022 10:19:51

%S 1,1,-1,-8,-7,96,385,-1210,-14943,-5912,593361,2409298,-22935647,

%T -236575468,590041257,20313729886,40488350401,-1659176093392,

%U -11796304552991,120680593857514,1966312603184321,-4949789957167124,-288454178376442407,-849587090710029098

%N Expansion of e.g.f. exp(x)^( cos(x) - sin(x) ).

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)^(cos(x)-sin(x))))

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^(j\2)*j*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A000248, A009189, A009214, A354545.

%K sign

%O 0,4

%A _Seiichi Manyama_, Aug 18 2022