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 A372738 #17 Jun 28 2024 22:26:08
%S A372738 1,4,28,298,4240,75394,1608688,40045618,1139279680,36463487554,
%T A372738 1296712045648,50724943433938,2164652356532320,100072984472662114,
%U A372738 4982304066392196208,265770533884409878258,15122101633293034668160,914210942121577873619074,58519992421072004957876368,3954059527570115477197922578
%N A372738 Binomial transform of A369795.
%F A372738 a(n) = Sum_{j=1..n} (1-(-1)^j-(-2)^j)*binomial(n,j)*a(n-j) for n > 0.
%F A372738 a(n) = 2^n + Sum_{j=1..n} (3^j-1)*binomial(n,j)*a(n-j).
%F A372738 a(n) = 1 + Sum_{j=1..n} (2^j-(-1)^j)*binomial(n,j)*a(n-j).
%F A372738 E.g.f.: exp(2*x)/(1 + exp(x) - exp(3*x)). - _Vaclav Kotesovec_, Jun 01 2024
%t A372738 nmax = 20; CoefficientList[Series[E^(2*x)/(1 + E^x - E^(3*x)), {x, 0, nmax}], x]*Range[0, nmax]! (* _Vaclav Kotesovec_, Jun 01 2024 *)
%o A372738 (SageMath)
%o A372738 def a(n):
%o A372738 if n==0:
%o A372738 return 1
%o A372738 else:
%o A372738 return sum([(1-(-1)^j-(-2)^j)*binomial(n,j)*a(n-j) for j in [1,..,n]])
%o A372738 list(a(n) for n in [0,..,20])
%Y A372738 Cf. A369795, A355408.
%K A372738 nonn
%O A372738 0,2
%A A372738 _Prabha Sivaramannair_, May 11 2024