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