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A001341 Expansion of e.g.f. 6*exp(x)/(1-x)^4.

%I A001341 M4205 N1755 #49 Jan 17 2025 09:42:51
%S A001341 6,30,174,1158,8742,74046,696750,7219974,81762438,1005151902,
%T A001341 13336264686,189992451270,2893180308774,46904155833918,
%U A001341 806663460996462,14669947577257926,281298999630211590,5672559830998316574,120014233288249367598,2658221288671765756422
%N A001341 Expansion of e.g.f. 6*exp(x)/(1-x)^4.
%D A001341 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001341 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001341 T. D. Noe, <a href="/A001341/b001341.txt">Table of n, a(n) for n = 0..100</a>
%H A001341 E. Biondi, L. Divieti, and G. Guardabassi, <a href="http://dx.doi.org/10.4153/CJM-1970-003-9">Counting paths, circuits, chains and cycles in graphs: A unified approach</a>, Canad. J. Math. 22 1970 22-35.
%H A001341 Philip Feinsilver and John McSorley, <a href="http://dx.doi.org/10.1155/2011/539030">Zeons, Permanents, the Johnson Scheme, and Generalized Derangements</a>, International Journal of Combinatorics, Volume 2011, Article ID 539030, 29 pages.
%F A001341 a(n) = ceiling( n!*(n^3 + 3*n^2 + 5*n + 2)*exp(1) ). - _Mark van Hoeij_, Nov 11 2009
%F A001341 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
%F A001341 a(n) = 6 * A095000(n). - _Alois P. Heinz_, Jan 17 2025
%t A001341 nn = 20; Range[0, nn]! CoefficientList[Series[6*Exp[x]/(1 - x)^4, {x, 0, nn}], x] (* _T. D. Noe_, Jun 28 2012 *)
%o A001341 (PARI) my(x='x+O('x^66)); Vec(serlaplace(6*exp(x)/(1-x)^4)) \\ _Joerg Arndt_, May 09 2013
%Y A001341 Cf. A095000.
%K A001341 nonn
%O A001341 0,1
%A A001341 _N. J. A. Sloane_ and _Simon Plouffe_
%E A001341 Error in definition corrected Jan 30 2008
%E A001341 More terms from _N. J. A. Sloane_, Jan 30 2008