A186639 a(n) = n!/2-(-2)^(n-2)*(n-2).

1, 0, 1, 5, 4, 84, 296, 2680, 19776, 182336, 1812352, 19963008, 239490560, 3113532928, 43589096448, 653837290496, 10461394714624, 177843714539520, 3201186851815424, 60822550206644224, 1216451004083601408, 25545471085864681472, 562000363888782868480, 12926008369442532360192, 310224200866619627405312, 7755605021665493184937984

Offset

0,4

Comments

"Number of positive terms in the ordinary development of a determinant having negative elements in the diagonal and positive elements elsewhere." [Muir]

References

T. Muir, A Treatise on the Theory of Determinants. Dover, NY, 1960, Sect. 132, p. 115.

Links

Table of n, a(n) for n=0..25.

Formula

E.g.f.: (1/(1 - x) + (1 + x)*exp(-2*x))/2. - Ilya Gutkovskiy, Aug 17 2016

Maple

f:=n->n!/2-(-2)^(n-2)*(n-2); [seq(f(n), n=0..40)];

Mathematica

Table[n!/2 - (-2)^(n - 2)*(n - 2), {n, 0, 25}] (* Wesley Ivan Hurt, Aug 17 2016 *)

Prog

(Magma) [Factorial(n)/2 - (-2)^(n - 2)*(n - 2) : n in [0..30]]; // Wesley Ivan Hurt, Aug 17 2016

Crossrefs

Sequence in context: A181613 A264880 A128191 * A266668 A043299 A144776

Adjacent sequences: A186636 A186637 A186638 * A186640 A186641 A186642

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 24 2011

Status

approved