0,3

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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).

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.

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.

(1/2)*(exp(2*x + x^2) + 1);

For Maple program see A000903.

Equals 1/2 * A000898(n) for n>0.

Sequence in context: A109085 A001002 A151062 this_sequence A151063 A103138 A074527

Adjacent sequences: A000899 A000900 A000901 this_sequence A000903 A000904 A000905

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)