A001341 E.g.f.: 6*exp(x)/(1-x)^4; (Formerly M4205 N1755)

6, 30, 174, 1158, 8742, 74046, 696750, 7219974, 81762438, 1005151902, 13336264686, 189992451270, 2893180308774, 46904155833918, 806663460996462, 14669947577257926, 281298999630211590, 5672559830998316574, 120014233288249367598, 2658221288671765756422

Offset

0,1

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.

Formula

a(n) = ceiling( n!*(n^3 + 3*n^2 + 5*n + 2)*exp(1) ). - Mark van Hoeij, Nov 11 2009

G.f.: Q(0)*(1-x)^2/x^3 - 2/x + 1/x^2 - 1/x^3, where Q(k)= 1 + (2*k + 1)*x/( 1 - x - 2*x*(1-x)*(k+1)/(2*x*(k+1) + (1-x)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 09 2013

Mathematica

nn = 20; Range[0, nn]! CoefficientList[Series[6*Exp[x]/(1 - x)^4, {x, 0, nn}], x] (* T. D. Noe, Jun 28 2012 *)

Prog

(PARI) x='x+O('x^66); Vec(serlaplace(6*exp(x)/(1-x)^4)) \\ Joerg Arndt, May 09 2013

Crossrefs

Sequence in context: A362810 A365273 A110706 * A089896 A057754 A001473

Adjacent sequences: A001338 A001339 A001340 * A001342 A001343 A001344

Keyword

nonn

Author

N. J. A. Sloane and Simon Plouffe

Extensions

Error in definition corrected Jan 30 2008

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

Status

approved