A001340 E.g.f.: 2*exp(x)/(1-x)^3. (Formerly M1858 N0736)

2, 8, 38, 212, 1370, 10112, 84158, 780908, 8000882, 89763320, 1094915222, 14431179908, 204423631178, 3097603939952, 50001759773870, 856665220770332, 15526612798028258, 296825612428239848, 5969385443426556422, 125983618731675924020, 2784204907403441680442

Offset

0,1

Comments

a(n) = A001339 (n+1) - A001339 (n)..3-1=2, 11-3=8, 49-11=38... [Gary Detlefs, Jun 06 2010]

References

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..100

E. Biondi, L. Divieti, G. Guardabassi, Counting paths, circuits, chains and cycles in graphs: A unified approach, Canad. J. Math. 22 1970 22-35.

Philip Feinsilver and John McSorley, Zeons, Permanents, the Johnson Scheme, and Generalized Derangements, International Journal of Combinatorics, Volume 2011, Article ID 539030, 29 pages; doi:10.1155/2011/539030.

Formula

a(n) = 2 * A082030(n).

a(n) = floor((n+1)*(n+1)!*e) - floor(n*n!*e) [Gary Detlefs, Jun 06 2010]

a(n) = {exp(1)*(n^2+n+1)*n!} for n>0, where {x} is the neareast integer, proposed by Simon Plouffe, March 1993.

G.f.: (1-x)/x/Q(0) -1/x, where Q(k)= 1 - x - x*(k+2)/(1 - x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 22 2013

G.f.: W(0)/x - 1/x, where W(k) = 1 - x*(k+2)/( x*(k+3) - 1/(1 - x*(k+1)/( x*(k+1) - 1/W(k+1) ))); (continued fraction). - Sergei N. Gladkovskii, Aug 26 2013

Conjecture: a(n) +(-n-3)*a(n-1) +(n-1)*a(n-2)=0. - R. J. Mathar, May 03 2017

Mathematica

nn = 20; Range[0, nn]! CoefficientList[Series[2*Exp[x]/(1 - x)^3, {x, 0, nn}], x] (* T. D. Noe, Jun 28 2012 *)

Crossrefs

Sequence in context: A108246 A020031 A179323 * A275707 A058786 A096654

Adjacent sequences: A001337 A001338 A001339 * A001341 A001342 A001343

Keyword

nonn,easy

Author

N. J. A. Sloane and Simon Plouffe

Extensions

Error in description corrected Jan 30 2008

More terms from N. J. A. Sloane, Jan 30 2008

Status

approved