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A002747
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Logarithmic numbers.
(Formerly M1924 N0759)
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1
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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; internal format)
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OFFSET
| 1,2
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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 (Gerald.McGarvey(AT)comcast.net), Jun 06 2004
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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).
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LINKS
| S. Plouffe, Inverter lookup on 1.8134302039235
Index entries for sequences related to logarithmic numbers
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FORMULA
| E.g.f.: x/exp(x)/(1-x^2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 09 2003
It appears that a(n)=n{(n-1)(a(n-2))-1^n}. - Matthew Vandermast (ghodges14(AT)comcast.net), 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 (Gerald.McGarvey(AT)comcast.net), Jun 06 2004
a(n)=(-1)^n*sum{k=0..n, binomial(n, k)k!(1-(-1)^k)/2} - Paul Barry (pbarry(AT)wit.ie), Sep 14 2004
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CROSSREFS
| Sequence in context: A098518 A086511 A138912 * A110377 A041877 A090208
Adjacent sequences: A002744 A002745 A002746 * A002748 A002749 A002750
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from J. O. Shallit.
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 09 2003
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