A279271 - OEIS

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

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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