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%I #15 May 08 2017 00:24:34
%S 1,1,3,12,57,320,2065,14954,119585,1044184,9867633,100185294,
%T 1086173121,12510549116,152422123321,1956974934290,26391647743937,
%U 372769201632784,5500416368181921,84594395013757398,1353277808896178145,22476374660911200068,386925983827921358665,6893254434792968631674
%N Exponential transform of the Pell numbers.
%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H Eric W. Weisstein MathWorld, <a href="http://mathworld.wolfram.com/ExponentialTransform.html">Exponential Transform</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PellNumber.html">Pell Number</a>
%F E.g.f.: exp(exp(x)*sinh(sqrt(2)*x)/sqrt(2)).
%e E.g.f.: A(x) = 1 + x/1! + 3*x^2/2! + 12*x^3/3! + 57*x^4/4! + 320*x^5/5! + 2065*x^6/6! + ...
%t Range[0, 23]! CoefficientList[Series[Exp[Exp[x] Sinh[Sqrt[2] x]/Sqrt[2]], {x, 0, 23}], x]
%o (PARI) x='x + O('x^30); round( Vec(serlaplace(exp(exp(x)*sinh(sqrt(2)*x) /sqrt(2)))) ) \\ _G. C. Greubel_, Dec 13 2016
%Y Cf. A000129, A256180.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 12 2016
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