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 A349541 #9 Nov 26 2021 05:16:00
%S A349541 1,5,41,301,2513,20181,170745,1423101,12161441,103344037,889924553,
%T A349541 7650373325,66271512433,574065261173,4996181205657,43511277885597,
%U A349541 380108373809985,3323551100483397,29122753514303337,255427680480306285,2243831648555990289,19728657265135701525
%N A349541 E.g.f.: exp(x) * (BesselI(0,8*x) + BesselI(1,8*x)).
%F A349541 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(k,floor(k/2)) * 4^k.
%F A349541 a(n) ~ 3^(2*n + 1) / (2*sqrt(Pi*n)). - _Vaclav Kotesovec_, Nov 26 2021
%t A349541 nmax = 21; CoefficientList[Series[Exp[x] (BesselI[0, 8 x] + BesselI[1, 8 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A349541 Table[Sum[Binomial[n, k] Binomial[k, Floor[k/2]] 4^k, {k, 0, n}], {n, 0, 21}]
%o A349541 (PARI) a(n) = sum(k=0, n, binomial(n,k) * binomial(k, k\2) * 4^k); \\ _Michel Marcus_, Nov 21 2021
%Y A349541 Cf. A001405, A005573, A005773, A151318, A349540.
%K A349541 nonn
%O A349541 0,2
%A A349541 _Ilya Gutkovskiy_, Nov 21 2021