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A009599 Expansion of e.g.f. sinh(sinh(x)*exp(x)). 5
0, 1, 2, 5, 20, 117, 782, 5441, 39496, 306921, 2602682, 24116413, 241121564, 2561633245, 28613237382, 334511450617, 4089814554384, 52302564139985, 699179303859698, 9751200460426357, 141494250613386916 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n, k)*(1-(-1)^k)/2*2^(n-k). - Vladeta Jovovic, Sep 26 2003
G.f.: Sum_{k>=0} x^(2*k+1)/Product_{i=0..2*k+1} (1 - 2*i*x). - Sergei N. Gladkovskii, Jan 06 2013
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
MATHEMATICA
Table[Sum[StirlingS2[n, k]*(1-(-1)^k)/2*2^(n-k), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 06 2014 after Vladeta Jovovic *)
Table[(BellB[n, 1/2] - BellB[n, -1/2]) 2^(n-1), {n, 0, 20}] (* Vladimir Reshetnikov, Nov 01 2015 *)
With[{nn=20}, CoefficientList[Series[Sinh[Sinh[x]Exp[x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jun 02 2017 *)
PROG
(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
CROSSREFS
Cf. A065143.
Sequence in context: A052850 A000130 A288841 * A112833 A144503 A012321
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Extended and signs tested by Olivier Gérard, Mar 15 1997
STATUS
approved

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Last modified May 26 18:19 EDT 2024. Contains 372840 sequences. (Running on oeis4.)