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 A002747 Logarithmic numbers. (Formerly M1924 N0759) 5
 1, -2, 9, -28, 185, -846, 7777, -47384, 559953, -4264570, 61594841, -562923252, 9608795209, -102452031878, 2017846993905, -24588487650736, 548854382342177, -7524077221125234, 187708198761024553, -2859149344027588940, 78837443479630312281, -1320926996940746090302 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n odd, lim n->inf a(n)/n! = cosh(1). For n even, lim n->inf a(n)/n! = sinh(1) lim n->inf n*a(n)*a(n-1)/n!^2 = cosh(1)sinh(1). For signed values, Sum n=1..inf a(n)/n!^2 = 0. For unsigned values, Sum n=1..inf a(n)/n!^2 = cosh(1)sinh(1). - Gerald McGarvey, Jun 06 2004 REFERENCES J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. 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 Alois P. Heinz, Table of n, a(n) for n = 1..200 J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. [Annotated scanned copy] Simon Plouffe, Inverter lookup on 1.8134302039235 FORMULA E.g.f.: x/exp(x)/(1-x^2). - Vladeta Jovovic, Feb 09 2003 a(n) = n*((n-1)*a(n-2)-(-1)^n). - Matthew Vandermast, Jun 30 2003 For n odd, n! * Sum_{i=0..n-1 i even} 1/i!, for n even, n! * Sum_{i=1..n-1, i odd} 1/i!. - Gerald McGarvey, Jun 06 2004 a(n) = (-1)^n*sum{k=0..n, C(n, k)k!(1-(-1)^k)/2}. - Paul Barry, Sep 14 2004 a(n) = (-1)^(n+1)*n*A087208(n-1). - R. J. Mathar, Jul 24 2015 a(n) = (exp(-1)*Gamma(1+n,-1) - (-1)^n*exp(1)*Gamma(1+n,1))/2 = (A000166(n) - (-1)^n*A000522(n))/2. - Peter Luschny, Dec 18 2017 MAPLE a:= proc(n) a(n):= n*`if`(n<2, n, (n-1)*a(n-2)-(-1)^n) end: seq(a(n), n=1..25);  # Alois P. Heinz, Jul 10 2013 MATHEMATICA egf = x/Exp[x]/(1-x^2); a[n_] := SeriesCoefficient[egf, {x, 0, n}]*n!; Table[a[n], {n, 1, 22}] (* Jean-François Alcover, Jan 17 2014, after Vladeta Jovovic *) a[n_] := (Exp[-1] Gamma[1 + n, -1] - (-1)^n Exp[1] Gamma[1 + n, 1])/2; Table[a[n], {n, 1, 22}] (* Peter Luschny, Dec 18 2017 *) CROSSREFS Cf. A000166, A000522, A087208. Sequence in context: A291632 A324372 A138912 * A110377 A041877 A090208 Adjacent sequences:  A002744 A002745 A002746 * A002748 A002749 A002750 KEYWORD sign AUTHOR EXTENSIONS More terms from Jeffrey Shallit. More terms from Vladeta Jovovic, Feb 09 2003 STATUS approved

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Last modified August 25 05:19 EDT 2019. Contains 326318 sequences. (Running on oeis4.)