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A368237
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Expansion of e.g.f. 1/(exp(-x) - 3*x).
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1
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1, 4, 31, 361, 5605, 108781, 2533447, 68836279, 2137543177, 74673228457, 2898494302651, 123757822391083, 5764497138070381, 290878956151681405, 15806942065094830735, 920336494043393536591, 57157621592164505969425, 3771643127452655490322513
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OFFSET
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0,2
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LINKS
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FORMULA
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a(0) = 1; a(n) = 3*n*a(n-1) + Sum_{k=1..n} (-1)^(k-1) * binomial(n,k) * a(n-k).
a(n) = n! * Sum_{k=0..n} 3^(n-k) * (n-k+1)^k / k!.
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MATHEMATICA
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a[n_] := n! Sum[3^(n - k) (n - k + 1)^k / k!, {k, 0, n}]; Table[a[n], {n, 0, 17}] (* or *) a[0] = 1; a[n_] := 3n a[n - 1] + Sum[(-1)^(k - 1) Binomial[n, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}] (* James C. McMahon, Dec 18 2023 *)
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PROG
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(PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*(n-k+1)^k/k!);
(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(exp(-x) - 3*x))) \\ Michel Marcus, Dec 18 2023
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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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