A294222 Exponential transform of the Lucas numbers (A000204).

1, 1, 4, 14, 69, 372, 2320, 15913, 119938, 978456, 8586177, 80456488, 800905726, 8429875989, 93453556378, 1087491751050, 13244265431889, 168370713583760, 2229127899764052, 30671277674880073, 437770190804865414, 6470590710038358164, 98891186448861721537, 1560548838446810788940, 25394750159240696915562

Offset: 0

Author

Ilya Gutkovskiy, Oct 25 2017

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x/1! + 4*x^2/2! + 14*x^3/3! + 69*x^4/4! + 372*x^5/5! + 2320*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 Weisstein's World of Mathematics, Exponential Transform
• Eric Weisstein's World of Mathematics, Lucas Number

Crossrefs

Cf. A000204, A256180, A279271.

Programs

Mathematica

Range[0, 24]! CoefficientList[Series[Exp[2 Exp[x/2] Cosh[Sqrt[5] x/2] - 2], {x, 0, 24}], x]
a[n_] := a[n] = Sum[a[n - k] Binomial[n - 1, k - 1] LucasL[k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 24}]

Formula

E.g.f.: exp(2*exp(x/2)*cosh(sqrt(5)*x/2) - 2).