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 A299121 #5 Feb 03 2018 04:34:55
%S A299121 1,2,3,6,38,1490,443762,965262242,23539096637282,4878608938121399042,
%T A299121 16752209028723653862101762,531115497554502361264846265433602,
%U A299121 392660148984369152453298787770243889113602,2811644066816242246665284589590844386691155533363202
%N A299121 a(n) = Sum_{k=0..n} (k*(n-k))!.
%F A299121 a(n) ~ sqrt(Pi) * n^(n^2/2 + 1) / (2^(n^2/2 + 1/2) * exp(n^2/4)) if n is even, and a(n) ~ sqrt(Pi) * n^(n^2/2 + 1/2) / (2^(n^2/2 - 1) * exp(n^2/4)) if n is odd.
%t A299121 Table[Sum[(k*(n-k))!, {k, 0, n}], {n, 0, 14}]
%Y A299121 Cf. A000142, A003149, A003422.
%K A299121 nonn
%O A299121 0,2
%A A299121 _Vaclav Kotesovec_, Feb 03 2018