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A328055 Expansion of e.g.f. -log(1 - x / (1 - x)^2). 1
0, 1, 5, 32, 270, 2904, 38400, 605520, 11113200, 232888320, 5488560000, 143704108800, 4138573824000, 130020673305600, 4425201196416000, 162194862064435200, 6369479157000960000, 266808274486161408000, 11874724379464826880000, 559591797303082672128000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

E.g.f.: log(1 + Sum_{k>=1} Fibonacci(2*k) * x^k).

a(n) = (n - 1)! * (Lucas(2*n) - 2) for n > 0.

MATHEMATICA

nmax = 19; CoefficientList[Series[-Log[1 - x/(1 - x)^2], {x, 0, nmax}], x] Range[0, nmax]!

Join[{0}, Table[(n - 1)! (LucasL[2 n] - 2), {n, 1, 19}]]

PROG

(MAGMA) [0] cat [Factorial(n - 1)*(Lucas(2*n)-2):n in [1..20]]; // Marius A. Burtea, Oct 03 2019

(PARI) my(x='x+O('x^20)); concat(0, Vec(serlaplace(-log(1 - x / (1 - x)^2)))) \\ Michel Marcus, Oct 03 2019

CROSSREFS

Cf. A001906, A004146, A005248, A005443, A029767, A052567 (exponential transform), A100404, A226968, A328054.

Sequence in context: A215916 A068102 A166993 * A265130 A305407 A320349

Adjacent sequences:  A328052 A328053 A328054 * A328056 A328057 A328058

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 03 2019

STATUS

approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)