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URL: https://oeis.org/A323721

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A323721
Expansion of e.g.f. log(2*exp(x/2)*cosh(sqrt(5)*x/2) - 1).
0
0, 1, 2, -3, -6, 50, -13, -1498, 6234, 59145, -748678, -1415238, 92962179, -411570250, -11993577118, 167710062977, 1224967301754, -51920085859710, 135335259830867, 14992073315394822, -201575378391009366, -3667884891055854535, 128570113943360964602, 209758874692705861322
OFFSET
0,3
FORMULA
E.g.f.: log(1 + Sum_{k>=1} Lucas(k)*x^k/k!).
a(0) = 0; a(n) = Lucas(n) - (1/n)*Sum_{k=1..n-1} binomial(n,k)*Lucas(n-k)*k*a(k).
MAPLE
seq(n!*coeff(series(log(2*exp(x/2)*cosh(sqrt(5)*x/2)-1), x=0, 24), x, n), n=0..23); # Paolo P. Lava, Jan 28 2019
MATHEMATICA
nmax = 23; CoefficientList[Series[Log[2 Exp[x/2] Cosh[Sqrt[5] x/2] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = LucasL[n] - Sum[Binomial[n, k] LucasL[n - k] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 23}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jan 25 2019
STATUS
approved