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A009599
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Expansion of e.g.f. sinh(sinh(x)*exp(x)).
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5
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0, 1, 2, 5, 20, 117, 782, 5441, 39496, 306921, 2602682, 24116413, 241121564, 2561633245, 28613237382, 334511450617, 4089814554384, 52302564139985, 699179303859698, 9751200460426357, 141494250613386916
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OFFSET
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0,3
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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.: x/( G(0)-x^2 ) where G(k) = x^2 + (4*x*k-1)*(4*x*k+2*x-1) - x^2*(4*x*k-1)*(4*x*k+2*x-1)/G(k+1); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 06 2013
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Sinh[Sinh[x]Exp[x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jun 02 2017 *)
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PROG
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(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(sinh(sinh(x)*exp(x))))) \\ G. C. Greubel, Jan 22 2018
(Magma) [(&+[2^(n-k)*StirlingSecond(n, k)*(1 - (-1)^k)/2: k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jan 22 2018
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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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