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A294214
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E.g.f.: exp(1/((1-x)*(1-x^2)*(1-x^3)) - 1).
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3
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1, 1, 5, 31, 241, 2261, 25501, 319915, 4564001, 71905321, 1240694101, 23250921431, 470598127825, 10200501671101, 236040247113581, 5800885227542371, 150850086300786241, 4137020164029442385, 119309846230265324581, 3608164806033723494671
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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) = a(n-1) + 2*(n-1)*n*a(n-2) + (n-2)*(n-1)*(2*n+1)*a(n-3) - (n-10)*(n-3)*(n-2)*(n-1)*a(n-4) - 4*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6) + 2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-7) + 2*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-8) - (n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-10). - Vaclav Kotesovec, Dec 02 2021
a(n) ~ exp(-101/144 + 29*n^(1/4)/(36*2^(3/4)) + sqrt(n/2) + 2^(7/4)*n^(3/4)/3 - n) * n^(n - 1/8) / 2^(9/8) * (1 + 71323/(103680*2^(1/4)*n^(1/4))). - Vaclav Kotesovec, Dec 02 2021
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MATHEMATICA
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nmax = 20; CoefficientList[Series[E^(1/((1-x)*(1-x^2)*(1-x^3)) - 1), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Dec 02 2021 *)
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(1/((1-x)*(1-x^2)*(1-x^3))-1)))
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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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