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 A277478 #7 Nov 08 2017 02:32:39
%S A277478 0,1,2,12,76,720,8766,131096,2319416,47361600,1096018330,28344108672,
%T A277478 810053677764,25352185339520,862335856149782,31674845755622400,
%U A277478 1249527587684729584,52687201308036059136,2364751154207006978994,112562199977955164819456
%N A277478 E.g.f.: -cosh(x)*LambertW(-x).
%H A277478 G. C. Greubel, <a href="/A277478/b277478.txt">Table of n, a(n) for n = 0..385</a>
%F A277478 a(n) = Sum_{k=1..n} (1 + (-1)^(n-k)) * binomial(n,k) * k^(k-1)/2.
%F A277478 a(n) ~ cosh(exp(-1)) * n^(n-1).
%t A277478 CoefficientList[Series[-Cosh[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
%t A277478 Table[Sum[(1 + (-1)^(n-k)) * Binomial[n, k] * k^(k-1)/2, {k, 1, n}], {n, 0, 20}]
%o A277478 (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-cosh(x)*lambertw(-x)))) \\ _G. C. Greubel_, Nov 07 2017
%Y A277478 Cf. A000169, A277464, A277473, A277476, A277477.
%K A277478 nonn
%O A277478 0,3
%A A277478 _Vaclav Kotesovec_, Oct 17 2016