A092170 Sum of squares of alternating factorials : n!^2 - (n-1)!^2 + (n-2)!^2 - ... 1!^2.

1, 3, 33, 543, 13857, 504543, 24897057, 1600805343, 130081089057, 13038108350943, 1580312813889057, 227862219988670943, 38547925823643969057, 7561506530728353470943, 1702450746193471070529057

Offset

1,2

Comments

The height of a regular simplex (hypertetrahedron) of dimension n and with unit length edges will be h(n)=sqrt(a(n))/n!. The contents (hypervolume) will then be V(n)=V(n-1)*h(n)/n where V(1)=1.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..253

Formula

a(n) = n!^2 - a(n-1), a(1)=1. - Charles R Greathouse IV, Oct 13 2004

Example

a(3)=3!^2-a(2)=36-a(2);
a(2)=2!^2-a(1)=4-a(1)=3-1=3 ->
a(3)=36-3=33.

Mathematica

a[n_] := Sum[(-1)^j*((n - j)!)^2, {j, 0, n - 1}]
Module[{nn=20, fctrls}, fctrls=(Range[nn]!)^2; Table[Total[Times@@@ Partition[ Riffle[Reverse[Take[fctrls, n]], {1, -1}, {2, -1, 2}], 2]], {n, nn}]] (* Harvey P. Dale, Aug 21 2016 *)

Crossrefs

Cf. A005165, A055546.

Sequence in context: A355795 A291818 A209245 * A083080 A002916 A009659

Adjacent sequences: A092167 A092168 A092169 * A092171 A092172 A092173

Keyword

easy,nonn

Author

Christer Mauritz Blomqvist (MauritzTortoise(AT)hotmail.com), Apr 01 2004

Status

approved