A354517 - OEIS

%I #16 Aug 17 2022 03:51:04

%S 1,0,-1,-3,-5,10,134,742,2325,-2820,-118756,-1138368,-7132025,

%T -20945990,196411214,4438271692,50498101545,400644382200,

%U 1571151012344,-16415635331328,-500300343321365,-7486919544207050,-81415563206142166,-563533196469890228

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

%F a(0) = 1; a(n) = -Sum_{k=1..n} A354519(k) * binomial(n-1,k-1) * a(n-k).

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

%o (PARI) a354519(n) = sum(k=1, n\2, ((-4)^k-(-16)^k)*bernfrac(2*k)/(2*k)*binomial(n, 2*k));

%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, a354519(j)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A000248, A009189, A215515, A354518, A354519.

%K sign

%O 0,4

%A _Seiichi Manyama_, Aug 16 2022