|
| |
|
|
A000902
|
|
E.g.f.: (1/2)*(exp(2x + x^2) + 1).
(Formerly M2853 N1147)
|
|
4
| |
|
|
1, 1, 3, 10, 38, 156, 692, 3256, 16200, 84496, 460592, 2611104, 15355232, 93376960, 585989952, 3786534784, 25152768128, 171474649344, 1198143415040, 8569374206464, 62668198184448, 468111364627456, 3568287053001728
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Number of solutions to the rook problem on a 2n X 2n board having a certain symmetry group (see Robinson for details).
One more than the number of ordered pairs of minimally intersecting partitions such that p consists of exactly two blocks.
|
|
|
REFERENCES
| L. C. Larson, The number of essentially different nonattacking rook arrangements, J. Recreat. Math., 7 (No. 3, 1974), circa pages 180-181.
R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
E. Lucas, Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1891, Vol. 1, p. 222.
B. Pittel, Where the typical set partitions meet and join, Electron. J. of Combin. 7, R5.
|
|
|
FORMULA
| a(n) = 2*a(n-1) + (2n-2)*a(n-2) for n >= 3. - N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2006
a(n) = 1 + n!/(2e) * [x^n] Sum[l>=0, 1/l! * {(1+x)^l-1}^2].
For asymptotics see the Robinson paper.
|
|
|
MAPLE
| (1/2)*(exp(2*x + x^2) + 1);
For Maple program see A000903.
|
|
|
MATHEMATICA
| n = 22; CoefficientList[ Series[(1/2)*(Exp[2*x+x^2] + 1), {x, 0, n}], x] * Table[k!, {k, 0, n}]
(* From Jean-François Alcover, May 18 2011 *)
|
|
|
CROSSREFS
| Equals 1/2 * A000898(n) for n>0.
Sequence in context: A109085 A001002 A151062 * A151063 A103138 A074527
Adjacent sequences: A000899 A000900 A000901 * A000903 A000904 A000905
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
|
| |
|
|
