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A009362
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Expansion of ln(1+sinh(x)/exp(x)).
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2
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0, 1, -3, 12, -66, 480, -4368, 47712, -608016, 8855040, -145083648, 2641216512, -52891055616, 1155444326400, -27344999497728, 696933753434112, -19031293222127616, 554336947975618560, -17155693983744196608
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = -Sum_{k>0} (-2*k)^n/3^k/k = -(-2)^n*polylog(-n+1, 1/3), n>0. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 30 2003
a(n) = -(-1)^n*Sum_{k=0..n-1} 3^k*Sum_{j=0..k} (-1)^j*(k-j)^n*C(n,j) for n>0. a(n) = -(-1)^n*Sum_{k=0..n-1} 3^k*A008292(n-1,k) for n>0, where A008292 are the Eulerian numbers. - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 29 2006
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MATHEMATICA
| Log[ 1+Sinh[ x ]/Exp[ x ] ]
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PROG
| (PARI) a(n)=-(-1)^n*sum(k=0, n-1, 3^k*sum(j=0, k, (-1)^j*(k-j)^(n-1)*binomial(n, j))) - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 29 2006
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CROSSREFS
| Cf. A008292 (Eulerian numbers).
Sequence in context: A199746 A080599 A120575 * A123227 A196556 A107713
Adjacent sequences: A009359 A009360 A009361 * A009363 A009364 A009365
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KEYWORD
| sign,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended with signs Mar 15 1997 by Olivier Gerard.
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