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A328286
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Expansion of e.g.f. -log(1 - x - x^2/2).
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0
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1, 2, 5, 21, 114, 780, 6390, 61110, 667800, 8210160, 112152600, 1685237400, 27624920400, 490572482400, 9381882510000, 192238348302000, 4201639474032000, 97572286427616000, 2399151995223984000, 62268748888378032000, 1701213856860117600000
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (n - 1)! * ((1 - sqrt(3))^n + (1 + sqrt(3))^n) / 2^n.
D-finite with recurrence +2*a(n) +2*(-n+1)*a(n-1) -(n-1)*(n-2)*a(n-2)=0. - R. J. Mathar, Aug 20 2021
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MAPLE
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b:= proc(n) b(n):= n! * (<<1|1>, <1/2|0>>^n)[1, 1] end:
a:= proc(n) option remember; `if`(n=0, 0, b(n)-add(
binomial(n, j)*j*b(n-j)*a(j), j=1..n-1)/n)
end:
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MATHEMATICA
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nmax = 21; CoefficientList[Series[-Log[1 - x - x^2/2], {x, 0, nmax}], x] Range[0, nmax]! // Rest
FullSimplify[Table[(n - 1)! ((1 - Sqrt[3])^n + (1 + Sqrt[3])^n)/2^n, {n, 1, 21}]]
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PROG
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(PARI) my(x='x+O('x^25)); Vec(serlaplace(-log(1 - x - x^2/2))) \\ Michel Marcus, Oct 11 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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