1,3

Number of set partitions of [n] into blocks of size 2 and 1 with at least one block of size 2. - Olivier GERARD (olivier.gerard(AT)gmail.com), Oct 29 2007

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).

R. B. Herrera, The number of elements of given period in finite symmetric group, Amer. Math. Monthly 64, 1957, 488-490.

L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Thanatipanonda, Thotsaporn, Inversions and major index for permutations, Math. Mag., No. 4, 2004

a(n) = b(n, 2), where b(n, d)=Sum_{k=1..n} (n-1)!/(n-k)! * Sum_{l:lcm{k, l}=d} b(n-k, l), b(0, 1)=1 is the number of degree-n permutations of order exactly d.

E.g.f.: -exp(x)+exp(x+1/2*x^2).

a(n) = a(n-1)+(1+a(n-2))*(n-1) = Sum_{j = 1 to floor[n/2]}[n!/(j!*(n-2j)!*(2^j))] = A000085(n)-1. - Henry Bottomley (se16(AT)btinternet.com), May 03 2001

Equals A000085 - 1. Cf. A001470 - A001473, A052501, A053496-A053504, A061121-A061128.

Sequence in context: A101499 A004665 A132835 this_sequence A101786 A012771 A120284

Adjacent sequences: A001186 A001187 A001188 this_sequence A001190 A001191 A001192

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 14 2001