A383316 - OEIS

%I #12 Apr 23 2025 10:29:22

%S 1,1,3,23,281,4593,93643,2285959,64981809,2107824353,76819828499,

%T 3107456481399,138145505435977,6694550810809297,351219409831557339,

%U 19832058937696108007,1199219012904515868257,77314609952787255980481,5293934640303567123132451

%N Expansion of e.g.f. exp(x/2) / (1-4*x)^(1/8).

%F a(n) = n! * Sum_{k=0..n} (-2)^k * (1/2)^(n-2*k) * binomial(-1/8,k)/(n-k)!.

%F a(n) = (4*n-3)*a(n-1) - 2*(n-1)*a(n-2) for n > 1.

%F a(n) ~ sqrt(Pi) * 2^(2*n + 1/2) * n^(n - 3/8) / (Gamma(1/8) * exp(n - 1/8)). - _Vaclav Kotesovec_, Apr 23 2025

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/2)/(1-4*x)^(1/8)))

%Y Cf. A002801, A383317.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 23 2025