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A334191
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a(n) = exp(1/3) * Sum_{k>=0} (3*k + 1)^n / ((-3)^k * k!).
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3
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1, 0, -3, -9, 0, 189, 1377, 4374, -26001, -560601, -4999482, -18631053, 235966365, 5966310960, 71037580689, 407585191059, -3965310883512, -157871090202975, -2631946996862451, -24922384546473810, 45577755305571339, 7795795206234609027, 192159735553383097014
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..22.
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FORMULA
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G.f.: (1/(1 - x)) * Sum_{k>=0} (-x/(1 - x))^k / Product_{j=1..k} (1 - 3*j*x/(1 - x)).
E.g.f.: exp(x + (1 - exp(3*x)) / 3).
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MATHEMATICA
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nmax = 22; CoefficientList[Series[1/(1 - x) Sum[(-x/(1 - x))^k/Product[(1 - 3 j x/(1 - x)), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 22; CoefficientList[Series[Exp[x + (1 - Exp[3 x])/3], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k] * 3^k * BellB[k, -1/3], {k, 0, n}], {n, 0, 22}] (* Vaclav Kotesovec, Apr 18 2020 *)
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CROSSREFS
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Column k=3 of A334192.
Cf. A003575, A293037, A317996, A334190.
Sequence in context: A021723 A206160 A112972 * A258147 A016673 A304022
Adjacent sequences: A334188 A334189 A334190 * A334192 A334193 A334194
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KEYWORD
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sign
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AUTHOR
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Ilya Gutkovskiy, Apr 18 2020
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STATUS
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approved
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