A279271 Exponential transform of the Pell numbers.

1, 1, 3, 12, 57, 320, 2065, 14954, 119585, 1044184, 9867633, 100185294, 1086173121, 12510549116, 152422123321, 1956974934290, 26391647743937, 372769201632784, 5500416368181921, 84594395013757398, 1353277808896178145, 22476374660911200068, 386925983827921358665, 6893254434792968631674

Offset: 0

Author

Ilya Gutkovskiy, Dec 12 2016

Keywords

• nonn

Examples

			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! + ...
		

Links

• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
• N. J. A. Sloane, Transforms
• Eric W. Weisstein MathWorld, Exponential Transform
• Eric Weisstein's World of Mathematics, Pell Number

Crossrefs

Cf. A000129, A256180.

Programs

Mathematica

Range[0, 23]! CoefficientList[Series[Exp[Exp[x] Sinh[Sqrt[2] x]/Sqrt[2]], {x, 0, 23}], x]

PARI

x='x + O('x^30); round( Vec(serlaplace(exp(exp(x)*sinh(sqrt(2)*x) /sqrt(2)))) ) \\ G. C. Greubel, Dec 13 2016

Formula

E.g.f.: exp(exp(x)*sinh(sqrt(2)*x)/sqrt(2)).