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A164575
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a(n) = n! * [x^n] 2*(tan(x))^2*(sec(x) + tan(x)).
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1
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0, 0, 4, 12, 56, 240, 1324, 7392, 49136, 337920, 2652244, 21660672, 196658216, 1859020800, 19192151164, 206057828352, 2385488163296, 28669154426880, 367966308562084, 4893320282898432, 68978503204900376, 1005520890400604160, 15445185289163949004, 244890632417194278912
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n-2) = |{up-down 2nd-max-upper permutations in S_n}| for n >= 2 (see Definition 3.4 in Kobayashi).
a(2*n) = 2*A225689(2*n) (see Lemma 4.2 in Kobayashi).
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MAPLE
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gf := (2*sin(x)*tan(x))/(1 - sin(x)): ser := series(gf, x, 25):
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MATHEMATICA
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CoefficientList[Series[2Tan[x]^2(Sec[x]+Tan[x]), {x, 0, 23}], x]*Table[n!, {n, 0, 23}]
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PROG
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(PARI) my(x='x+O('x^30)); concat([0, 0], Vec(serlaplace(2*(tan(x))^2*(1/cos(x) + tan(x))))) \\ Michel Marcus, Aug 13 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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