A013520 A problem in derangements.

0, 2, 9, 100, 1237, 18896, 337663, 6941194, 161357425, 4186540456, 119942830785, 3761004532550, 128121728853479, 4711881688294652, 186065500280409423, 7852240169544076190, 352684377274345906213, 16798134072300013751064

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Frank Schmidt and Rodica Simion, Card shuffling and a transformation on S_n, Aequationes Math. 44 (1992), no. 1, 11-34.

Formula

The reference gives a generating function.

Maple

a := n->simplify((n-1)!*sum(n^k/k!, k=0..n-1)-2*(n-1)^(n-1)): b := simplify(x^2+sum(a(n)*x^n/n!, n=3..70)): f := simplify(exp(b)): fser := simplify(series(f, x=0, 27)): s := seq(simplify(n!*coeff(fser, x^n)), n=1..25); # Emeric Deutsch, Mar 09 2004

Crossrefs

Sequence in context: A322645 A368725 A277180 * A378045 A369673 A041239

Adjacent sequences: A013517 A013518 A013519 * A013521 A013522 A013523

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Mar 09 2004

Status

approved