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 A308876 #15 Sep 18 2019 19:05:06
%S A308876 1,2,7,40,317,3166,37987,531812,8508985,153161722,3063234431,
%T A308876 67391157472,1617387779317,42052082262230,1177458303342427,
%U A308876 35323749100272796,1130359971208729457,38432239021096801522,1383560604759484854775,52575302980860424481432
%N A308876 Expansion of e.g.f. exp(x)*(1 - x)/(1 - 2*x).
%C A308876 Binomial transform of A002866.
%H A308876 Alois P. Heinz, <a href="/A308876/b308876.txt">Table of n, a(n) for n = 0..403</a>
%F A308876 a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 2^(k-1) * k!.
%F A308876 a(n) = A010844(n) - A067273(n).
%F A308876 a(n) ~ n! * 2^(n-1) * exp(1/2). - _Vaclav Kotesovec_, Jun 29 2019
%F A308876 a(n) = Sum_{k=0..n} k! * A271705(n,k). - _Alois P. Heinz_, Sep 12 2019
%p A308876 a:= n-> n! * add(ceil(2^(n-k-1))/k!, k=0..n):
%p A308876 seq(a(n), n=0..23); # _Alois P. Heinz_, Sep 12 2019
%t A308876 nmax = 19; CoefficientList[Series[Exp[x] (1 - x)/(1 - 2 x), {x, 0, nmax}], x] Range[0, nmax]!
%t A308876 Table[1 + Sum[Binomial[n,k] 2^(k - 1) k!, {k, 1, n}], {n, 0, 19}]
%Y A308876 Cf. A002866, A010844, A011782, A067273, A161936, A271705, A294466, A327606.
%Y A308876 Row sums of A326659.
%K A308876 nonn
%O A308876 0,2
%A A308876 _Ilya Gutkovskiy_, Jun 29 2019