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A355372
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Expansion of the e.g.f. log((1 - x) / (1 - 2*x)) / (1 - x)^3.
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4
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0, 1, 9, 77, 714, 7374, 85272, 1102968, 15908400, 254866320, 4516084800, 88102382400, 1883199024000, 43885950595200, 1109416142822400, 30273281955302400, 887493144729139200, 27827941161784780800, 929449073791558656000, 32943696020637889536000, 1234946945823695419392000
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OFFSET
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0,3
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COMMENTS
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Conjecture: For p prime, a(p) == -1 (mod p).
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(k+1)*k!*A062139(n, k + 1).
a(0) = 0, a(n) = n!*Sum_{k=1..n} (n-k+2)*(n-k+1)*(2^k-1)/(2*k).
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MAPLE
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seq(simplify(A355372(n)), n = 0..20);
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MATHEMATICA
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CoefficientList[Series[Log[(1 - x)/(1 - 2*x)]/ (1 - x)^3, {x, 0, 20}], x]Table[n!, {n, 0, 20}] (* Stefano Spezia, Jun 30 2022 *)
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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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