A280556 - OEIS

%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