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

0,3

Links

Table of n, a(n) for n=0..24.

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

Formula

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

Example

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! + ...

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}]

Crossrefs

Cf. A000204, A256180, A279271.

Sequence in context: A301511 A014512 A274804 * A005501 A065606 A049372

Adjacent sequences: A294219 A294220 A294221 * A294223 A294224 A294225

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 25 2017

Status

approved