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

0,3

Links

Table of n, a(n) for n=0..23.

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

Formula

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

Example

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! + ...

Mathematica

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

Prog

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

Crossrefs

Cf. A000129, A256180.

Sequence in context: A027710 A307495 A302101 * A293469 A009248 A012709

Adjacent sequences: A279268 A279269 A279270 * A279272 A279273 A279274

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 12 2016

Status

approved