This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381506 #13 Apr 23 2025 10:12:13
%S A381506 1,1,2,12,138,2202,44172,1064664,29947644,962720316,34812065304,
%T A381506 1398413067984,61779789904248,2976866834860728,155364530441352912,
%U A381506 8730749828092965408,525584335643810008848,33743905825099188235536,2301524700814009677800736
%N A381506 Expansion of e.g.f. exp(3*x/4) / (1-4*x)^(1/16).
%F A381506 a(n) = n! * Sum_{k=0..n} (-4)^k * (3/4)^(n-k) * binomial(-1/16,k)/(n-k)!.
%F A381506 a(n) = (4*n-3)*a(n-1) - 3*(n-1)*a(n-2) for n > 1.
%F A381506 a(n) ~ sqrt(Pi) * n^(n - 7/16) * 2^(2*n + 1/2) / (Gamma(1/16) * exp(n - 3/16)). - _Vaclav Kotesovec_, Apr 23 2025
%o A381506 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3*x/4)/(1-4*x)^(1/16)))
%Y A381506 Cf. A002801, A381505.
%K A381506 nonn
%O A381506 0,3
%A A381506 _Seiichi Manyama_, Apr 23 2025