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A009305
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E.g.f. log(1+x*cosh(x)).
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0
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0, 1, -1, 5, -18, 89, -600, 4717, -42896, 449073, -5287680, 69090581, -993391872, 15583801609, -264816161792, 4846181282685, -95022445824000, 1987373846425697, -44163232640630784, 1039121484066627877, -25807915421845422080, 674707915373741222841
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| a(n)=n!*sum(k=1..n-1, sum(i=0..k, (k-2*i)^(n-k)*binomial(k,i))/(2^k*(n-k)!)*(-1)^(k-1)/k)+(-1)^(n-1)*(n-1)!. [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 21 2011]
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MATHEMATICA
| Log[ 1+Cosh[ x ]*x ]
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PROG
| (Maxima)
a(n):=n!*sum(sum((k-2*i)^(n-k)*binomial(k, i), i, 0, k)/(2^k*(n-k)!)*(-1)^(k-1)/k, k, 1, n-1)+(-1)^(n-1)*(n-1)!; [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 21 2011]
(Pari) x='x+O('x^66); /* that many terms */
egf=log(1+x*cosh(x)); /* = x - 1/2*x^2 + 5/6*x^3 - 3/4*x^4 + 89/120*x^5 +-... */
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 21 2011 */
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CROSSREFS
| Sequence in context: A188206 A156305 A151490 * A097574 A113023 A174082
Adjacent sequences: A009302 A009303 A009304 * A009306 A009307 A009308
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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.
Definition corrected by Joerg Arndt, Apr 21 2011.
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