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 A369795 #33 Feb 26 2024 12:39:52
%S A369795 1,3,21,225,3201,56913,1214361,30229545,860016801,27525472353,
%T A369795 978858962601,38291126920665,1634047719138801,75542860973042193,
%U A369795 3761030066169432441,200624240375801784585,11415336789685550907201,690117422445926970890433,44175435307592982599575881
%N A369795 Binomial transform of A355408.
%F A369795 a(n) = 1 + Sum_{k=1..n} (3^k - 1) * binomial(n,k) * a(n-k) for n > 0.
%F A369795 E.g.f.: exp(x)/(1 + exp(x) - exp(3*x)). - _Vaclav Kotesovec_, Feb 01 2024
%t A369795 nmax = 20; CoefficientList[Series[E^x/(1 + E^x - E^(3*x)), {x, 0, nmax}], x]*
%t A369795 Range[0, nmax]! (* _Vaclav Kotesovec_, Feb 01 2024*)
%o A369795 (SageMath)
%o A369795 def a(m):
%o A369795 if m==0:
%o A369795 return 1
%o A369795 else:
%o A369795 return 1+sum([(3^j-1)*binomial(m,j)*a(m-j) for j in [1,..,m]])
%o A369795 list(a(m) for m in [1,..,50])
%Y A369795 Cf. A355408.
%K A369795 nonn
%O A369795 0,2
%A A369795 _Prabha Sivaramannair_, Feb 01 2024