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A001341
E.g.f.: 6*exp(x)/(1-x)^4;
(Formerly M4205 N1755)
3
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
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
KEYWORD
nonn
EXTENSIONS
Error in definition corrected Jan 30 2008
More terms from N. J. A. Sloane, Jan 30 2008
STATUS
approved