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A246607
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Expansion of e.g.f. exp(x - x^3).
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5
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1, 1, 1, -5, -23, -59, 241, 2311, 9745, -30743, -529919, -3161069, 6984121, 216832045, 1696212337, -2117117729, -138721306079, -1359994188719, 367573878145, 127713732858667, 1523067770484361, 1104033549399061, -159815269852521359, -2270787199743845705, -3946710127731620303
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-2*k,k)/(n-2*k)!.
a(n) = a(n-1) - 3! * binomial(n-1,2) * a(n-3) for n > 2. (End)
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MATHEMATICA
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PROG
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(PARI) default(seriesprecision, 30); serlaplace(exp(x-x^3)) \\ Michel Marcus, Aug 31 2014
(PARI) a(n) = n!*sum(k=0, n\3, (-1)^k*binomial(n-2*k, k)/(n-2*k)!); \\ Seiichi Manyama, Feb 25 2022
(PARI) a(n) = if(n<3, 1, a(n-1)-3!*binomial(n-1, 2)*a(n-3)); \\ Seiichi Manyama, Feb 25 2022
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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