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

0,2

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.

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

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 *)

Prog

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

Crossrefs

Cf. A052520, A055533.

Sequence in context: A178884 A211319 A121768 * A198960 A289263 A296600

Adjacent sequences: A280553 A280554 A280555 * A280557 A280558 A280559

Keyword

nonn

Author

Michel Marcus, Jan 05 2017

Status

approved