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A009153
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Expansion of e.g.f. cosh(sinh(x)*exp(x)).
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4
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1, 0, 1, 6, 29, 140, 757, 4858, 36409, 302520, 2681769, 25018510, 245905365, 2559272196, 28264854685, 330408571202, 4065526003313, 52349977261040, 702393407898705, 9795673312888214, 141820637175889805
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Stirling2(n, k)*(1+(-1)^k)/2*2^(n-k). - Vladeta Jovovic, Sep 26 2003
G.f.: 1 + x^2/( G(0)-x^2 ) where G(k) = x^2 + (4*x*k+2*x-1)*(4*x*k+4*x-1) - x^2*(4*x*k+2*x-1)*(4*x*k+4*x-1)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Jan 06 2013
a(n) ~ cosh(exp(r)*sinh(r)) * n^(n+1/2) / (r^(n+1/2) * exp(n+r) * sqrt(exp(2*r) * r * sech(exp(r)*sinh(r))^2 + (1+2*r) * tanh(exp(r)*sinh(r)))), where r is the root of the equation r*exp(r)*(cosh(r) + sinh(r))*tanh(exp(r)*sinh(r)) = n. - Vaclav Kotesovec, Aug 06 2014
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MATHEMATICA
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CoefficientList[Series[Cosh[Sinh[x]*E^x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Aug 06 2014 *)
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PROG
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(PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*(1+(-1)^k)/2*2^(n-k)); \\ Michel Marcus, Nov 02 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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