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 A292897 #7 Jul 05 2018 08:03:11
%S A292897 3,7,27,129,755,5187,40923,364333,3611811,39448095,470573723,
%T A292897 6086754297,84847445907,1267953887899,20220829211355,342759892460517,
%U A292897 6153802869270083,116652857267320503,2328215691932062491,48800672765792988145,1071780020853500289843
%N A292897 a(n) = -Sum_{k=1..3}(-1)^(n-k)*hypergeom([k, k-n-3], [], 1).
%F A292897 a(n) = A292898(3, n).
%F A292897 From _Vaclav Kotesovec_, Jul 05 2018: (Start)
%F A292897 Recurrence: (5*n^2 - 6*n + 4)*a(n) = (5*n^3 - n^2 - 6*n + 9)*a(n-1) + (n-1)*(5*n^2 + 4*n + 3)*a(n-2).
%F A292897 a(n) ~ 5*sqrt(Pi/2) * n^(n + 5/2) / exp(n+1). (End)
%p A292897 A292897 := n -> -add((-1)^(n-k)*hypergeom([k, k-n-3], [], 1), k=1..3):
%p A292897 seq(simplify(A292897(n)), n=0..20);
%t A292897 Table[-Sum[(-1)^(n-k)*HypergeometricPFQ[{k, k-n-3}, {}, 1], {k,1,3}], {n,0,20}] (* _Vaclav Kotesovec_, Jul 05 2018 *)
%Y A292897 Cf. A000166 (m=1), A259834 (m=2), this sequence (m=3), A292898 (m>=1).
%K A292897 nonn
%O A292897 0,1
%A A292897 _Peter Luschny_, Oct 05 2017