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A331339 E.g.f.: 1 / (1 + log(1 - x - x^2)). 0
1, 1, 5, 32, 292, 3294, 44918, 714468, 13002456, 266275200, 6060498672, 151750887936, 4145522908272, 122690391196944, 3910569680464848, 133549150323123744, 4864927063250290176, 188297220693251438208, 7716800776602560577408 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k - 1)! * Lucas(k) * a(n-k).

a(n) ~ n! * 2^(n+1) * exp(n/2) / (sqrt(5*exp(1) - 4) * (sqrt(5*exp(1) - 4) - exp(1/2))^(n+1)). - Vaclav Kotesovec, Jan 26 2020

MATHEMATICA

nmax = 18; CoefficientList[Series[1/(1 + Log[1 - x - x^2]), {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (k - 1)! LucasL[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]

CROSSREFS

Cf. A000204, A007840, A039647.

Sequence in context: A001923 A257710 A305305 * A307497 A023880 A104031

Adjacent sequences:  A331336 A331337 A331338 * A331340 A331341 A331342

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 14 2020

STATUS

approved

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Last modified September 21 10:03 EDT 2020. Contains 337268 sequences. (Running on oeis4.)