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 A343582 #9 Apr 24 2021 03:55:25
%S A343582 1,1,5,-3,105,-807,10413,-143595,2304081,-41453775,829134549,
%T A343582 -18240782931,437779321785,-11382260772087,318703306401405,
%U A343582 -9561099177693243,305955173729230497,-10402475906664696735,374489132640316502949,-14230587040330864850595,569223481613238080808201
%N A343582 a(n) = (-1)^n*n!*[x^n] exp(-3*x)/(1 - 2*x).
%C A343582 The row polynomials of the rencontres numbers (A008290) evaluated at -1/2 and normalized by (-2)^n.
%F A343582 a(n) = (-2)^n*Sum_{k=0..n} binomial(n, k)*subfactorial(n - k)*(-1/2)^k.
%F A343582 a(n) = 6*(n - 1)*a(n - 2) - (2*n - 3)*a(n - 1) for n >= 3.
%p A343582 egf := exp(-3*x)/(1 - 2*x): ser := series(egf, x, 32):
%p A343582 seq((-1)^n*n!*coeff(ser, x, n), n=0..20);
%t A343582 a[n_] := (-2)^n Sum[Binomial[n, k] Subfactorial[n - k] (-2)^(-k), {k, 0, n}];
%t A343582 Table[a[n], {n, 0, 20}]
%o A343582 (Python)
%o A343582 def A343582():
%o A343582 a, b, n = 1, 5, 3
%o A343582 yield 1
%o A343582 yield a
%o A343582 while True:
%o A343582 yield b
%o A343582 a, b = b, 6*(n - 1)*a - (2*n - 3)*b
%o A343582 n += 1
%o A343582 a = A343582(); print([next(a) for _ in range(21)])
%Y A343582 Cf. A008290, A000166, A000354.
%K A343582 sign
%O A343582 0,3
%A A343582 _Peter Luschny_, Apr 24 2021