A093345 a(n) = n! * {1 + Sum[i=1..n, 1/i*Sum(j=0..i-1, 1/j!)]}.

1, 2, 6, 23, 108, 605, 3956, 29649, 250892, 2367629, 24662700, 281153801, 3482350724, 46572620757, 668943488084, 10271127486065, 167892667249116, 2911049382788189, 53365747562592092, 1031352659792534169

Offset

0,2

Comments

Number of {12,2*1}-avoiding signed permutations in the hyperoctahedral group B_n.

Links

Table of n, a(n) for n=0..19.

D. Daly and L. Pudwell, Pattern avoidance in rook monoids, 2013. - From N. J. A. Sloane, Feb 03 2013

T. Mansour and J. West, Avoiding 2-letter signed patterns, arXiv:math/0207204 [math.CO], 2002.

Formula

E.g.f.: (exp(1)*(Ei(1, 1-x)-Ei(1, 1))+1)/(1-x). a(n) = n!*(1+Sum(A000522(i-1)/i!, i =1..n)). - Vladeta Jovovic, Apr 27 2004

Conjecture: a(n) -2*n*a(n-1) +(n^2-2)*a(n-2) -(n-2)^2*a(n-3)=0. - R. J. Mathar, May 30 2014

Mathematica

a[n_] := n! (1+Sum[1/i Sum[1/j!, {j, 0, i-1}], {i, 1, n}])
Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Oct 05 2018 *)

Prog

(PARI) a(n)=n!+n!*sum(i=1, n, 1/i*sum(j=0, i-1, 1/j!))

Crossrefs

Cf. A000774.

Cf. A000522, A093344.

Contribution from Johannes W. Meijer, Oct 16 2009: (Start)

Equals row sums of A165675.

(End)

Sequence in context: A071076 A297196 A112501 * A289681 A002136 A328441

Adjacent sequences: A093342 A093343 A093344 * A093346 A093347 A093348

Keyword

nonn

Author

Ralf Stephan, Apr 26 2004

Status

approved