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A002741
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Logarithmic numbers: expansion of -ln(1 - x) e^{-x}.
(Formerly M0037 N0010)
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3
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0, 1, -1, 2, 0, 9, 35, 230, 1624, 13209, 120287, 1214674, 13469896, 162744945, 2128047987, 29943053062, 451123462672, 7245940789073, 123604151490591, 2231697509543362
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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
| T. D. Noe, Table of n, a(n) for n=0..100
Index entries for sequences related to logarithmic numbers
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FORMULA
| E.g.f.: -ln(1 - x) / e^x. a(n) = (n-2) * a(n-1) + (n-1) * a(n-2) - (-1)^n, n>0. A000757(n) = (-1)^n + a(n). - Michael Somos Jun 21 2002
a(n) = n-th forward difference of [0, 1, 1, 2, 6, 24, ...] (factorials A000142 with 0 prepended). - Michael Somos Mar 28 2011
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EXAMPLE
| a(3) = 2 = 2! - 3*1! + 3*0! - 0. a(4) = 0 = 3! - 4*2! + 6*1! - 4*0! + 0. - Michael Somos Mar 28 2011
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MATHEMATICA
| a[n_] := Sum[(-1)^k*n!/((n-k)*k!), {k, 0, n-1}]; Table[a[n], {n, 0, 19}](* From Jean-François Alcover, Nov 21 2011 *)
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PROG
| (PARI) {a(n) = if( n<0, 0, sum( k=0, n-1, (-1)^k * binomial( n, k) * (n - k - 1)!))} /* Michael Somos Jun 21 2002 */
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CROSSREFS
| Cf. A000142, A000757.
Sequence in context: A083864 A154937 A037996 * A151887 A070681 A061189
Adjacent sequences: A002738 A002739 A002740 * A002742 A002743 A002744
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KEYWORD
| sign,easy,nice
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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.
Additional comments from Michael Somos, Jun 21, 2002
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