A294222 - OEIS

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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

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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.