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 A280556 #46 Jun 05 2017 16:21:15 %S A280556 0,2,26,242,2162,20162,201602,2177282,25401602,319334402,4311014402, %T A280556 62270208002,958961203202,15692092416002,271996268544002, %U A280556 4979623993344002,96035605585920002,1946321606541312002,41359334139002880002,919636959090769920002,21356013827774545920002 %N A280556 a(n) = Sum_{k=1..n} k^2 * (k+1)!. %C A280556 Partial sums of 2*A055533. %H A280556 Seiichi Manyama, <a href="/A280556/b280556.txt">Table of n, a(n) for n = 0..446</a> %H A280556 Mathematical Reflections, <a href="https://www.awesomemath.org/wp-pdf-files/math-reflections/mr-2013-01/mr_1_2013_problems.pdf">Problem J256</a>, Issue 1, 2013, p 4. %H A280556 Mathematical Reflections, <a href="https://www.awesomemath.org/wp-pdf-files/math-reflections/mr-2013-02/mr_1_2013_solutions.pdf">Solution to Problem J256</a>, Issue 2, 2013, p 4. %F A280556 a(n) = (n - 1)*(n + 2)! + 2 (see 2nd Mathematical Reflections link). Cf. A052520. %F A280556 E.g.f.: 2*exp(x) - 2*(1 - 4*x)/(1 - x)^4. - _Ilya Gutkovskiy_, Jan 05 2017 %p A280556 A280556:=n->add(k^2*(k+1)!, k=1..n): seq(A280556(n), n=0..30); # _Wesley Ivan Hurt_, Jan 05 2017 %t A280556 Table[Sum[k^2 (k+1)!,{k,n}],{n,0,20}] (* _Harvey P. Dale_, Jun 05 2017 *) %o A280556 (PARI) a(n) = sum(k=1, n, k^2*(k+1)!) %Y A280556 Cf. A052520, A055533. %K A280556 nonn %O A280556 0,2 %A A280556 _Michel Marcus_, Jan 05 2017