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 A349540 #9 Nov 26 2021 05:17:54
%S A349540 1,4,25,145,931,5866,38359,249880,1655035,10968724,73320259,491001721,
%T A349540 3304488565,22283168350,150744668065,1021597533865,6938921001235,
%U A349540 47202858834100,321640950882475,2194500145215595,14992297096036345,102535471011848230,702004865920831525
%N A349540 E.g.f.: exp(x) * (BesselI(0,6*x) + BesselI(1,6*x)).
%F A349540 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(k,floor(k/2)) * 3^k.
%F A349540 a(n) ~ 7^(n + 1/2) / sqrt(3*Pi*n). - _Vaclav Kotesovec_, Nov 26 2021
%t A349540 nmax = 22; CoefficientList[Series[Exp[x] (BesselI[0, 6 x] + BesselI[1, 6 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A349540 Table[Sum[Binomial[n, k] Binomial[k, Floor[k/2]] 3^k, {k, 0, n}], {n, 0, 22}]
%o A349540 (PARI) a(n) = sum(k=0, n, binomial(n,k) * binomial(k, k\2) * 3^k); \\ _Michel Marcus_, Nov 21 2021
%Y A349540 Cf. A001405, A005773, A026378, A151318, A349541.
%K A349540 nonn
%O A349540 0,2
%A A349540 _Ilya Gutkovskiy_, Nov 21 2021