A383313 - OEIS

%I #12 Apr 23 2025 05:42:22

%S 1,0,1,4,27,232,2455,30852,449113,7432624,137829249,2830911220,

%T 63796168579,1565078980536,41521403685463,1184510408920468,

%U 36158133322895985,1176012432875399008,40599110984252798017,1482736219224857910756,57115359439245403771051

%N Expansion of e.g.f. exp(-x/2) / (1-2*x)^(1/4).

%F a(n) = (-1)^n * n! * Sum_{k=0..n} (1/2)^(n-2*k) * binomial(-1/4,k)/(n-k)!.

%F a(n) = (n-1) * (2*a(n-1) + a(n-2)) for n > 1.

%F a(n) ~ sqrt(Pi) * 2^(n + 1/2) * n^(n - 1/4) / (Gamma(1/4) * exp(n + 1/4)). - _Vaclav Kotesovec_, Apr 23 2025

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x/2)/(1-2*x)^(1/4)))

%Y Cf. A383314, A383315.

%Y Cf. A002801.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Apr 23 2025