A026243 a(n) = A000522(n) - 2.

0, 3, 14, 63, 324, 1955, 13698, 109599, 986408, 9864099, 108505110, 1302061343, 16926797484, 236975164803, 3554627472074, 56874039553215, 966858672404688, 17403456103284419, 330665665962403998, 6613313319248079999, 138879579704209680020, 3055350753492612960483

Offset: 1

Author

N. J. A. Sloane, based on a message from a correspondent who wishes to remain anonymous, Dec 21 2003

Keywords

• nonn

Comments

Number of operations of addition and multiplication needed to evaluate a determinant of order n by cofactor expansion.

Examples

			To calculate a determinant of order 3:
    |a b c|       |e f|       |d f|       |d e|
D = |d e f| = a * |h i| - b * |g i| + c * |g h| =
    |g h i|
   = a * (e*i - f*h) - b * (d*i - f*g) + c * (d*h - e*g).
There are 9 multiplications * and 5 additions (+ or -), so 14 operations and a(3) = 14. - _Bernard Schott_, Apr 21 2019
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..170
• C. Dubbs and D. Siegel, Computing determinants, College Math. J., 18 (1987), 48-49.
• A. R. Pargeter, The vanishing coffee morning, Math. Gaz., 76 (1992), 386-387.
• P. G. Sawtelle, The ubiquitous e, Math. Mag., 49 (1976), 244-245. [_N. J. A. Sloane_, Jan 29 2009]

Crossrefs

Cf. A000522, A007526. Equals A033312 + A038156.

Cf. A001339.

Programs

Maple

a:= proc(n) a(n):= n*(a(n-1)+2)-1: end: a(1):= 0:
seq (a(n), n=1..30);  # Alois P. Heinz, May 25 2012

Mathematica

Table[E*Gamma[n+1, 1] - 2, {n, 1, 30}] (* Jean-François Alcover, May 18 2018 *)

Formula

a(n) = n*(a(n-1)+2)-1 for n>1, a(1) = 0. - Alois P. Heinz, May 25 2012

Conjecture: a(n) +(-n-2)*a(n-1) +(2*n-1)*a(n-2) +(-n+2)*a(n-3)=0. - R. J. Mathar, Jun 23 2013 [Confirmed by Altug Alkan, May 18 2018]

a(n) = floor(e*n!) - 2. - Bernard Schott, Apr 21 2019