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A279271 Exponential transform of the Pell numbers. 2
1, 1, 3, 12, 57, 320, 2065, 14954, 119585, 1044184, 9867633, 100185294, 1086173121, 12510549116, 152422123321, 1956974934290, 26391647743937, 372769201632784, 5500416368181921, 84594395013757398, 1353277808896178145, 22476374660911200068, 386925983827921358665, 6893254434792968631674 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 15 06:05 EST 2019. Contains 329144 sequences. (Running on oeis4.)