A280556 a(n) = Sum_{k=1..n} k^2 * (k+1)!.

0, 2, 26, 242, 2162, 20162, 201602, 2177282, 25401602, 319334402, 4311014402, 62270208002, 958961203202, 15692092416002, 271996268544002, 4979623993344002, 96035605585920002, 1946321606541312002, 41359334139002880002, 919636959090769920002, 21356013827774545920002

Offset: 0

Author

Michel Marcus, Jan 05 2017

Keywords

• nonn

Comments

Partial sums of 2*A055533.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..446
• Mathematical Reflections, Problem J256, Issue 1, 2013, p 4.
• Mathematical Reflections, Solution to Problem J256, Issue 2, 2013, p 4.

Crossrefs

Cf. A052520, A055533.

Programs

Maple

A280556:=n->add(k^2*(k+1)!, k=1..n): seq(A280556(n), n=0..30); # Wesley Ivan Hurt, Jan 05 2017

Mathematica

Table[Sum[k^2 (k+1)!,{k,n}],{n,0,20}] (* Harvey P. Dale, Jun 05 2017 *)

PARI

a(n) = sum(k=1, n, k^2*(k+1)!)

Formula

a(n) = (n - 1)*(n + 2)! + 2 (see 2nd Mathematical Reflections link). Cf. A052520.

E.g.f.: 2*exp(x) - 2*(1 - 4*x)/(1 - x)^4. - Ilya Gutkovskiy, Jan 05 2017