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A294215
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E.g.f.: exp(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) - 1).
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3
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1, 1, 5, 31, 265, 2501, 29461, 383755, 5721521, 93393865, 1683745381, 32835673751, 693498302905, 15671281854541, 378500195728565, 9704429057721091, 263513260349418721, 7544370749942882705, 227236831102901587141, 7177550671651275241615
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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+16) = (n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(n+7)*(n+8)*(n+9)*(n+10)*(n+11)*(n+12)*(n+13)*(n+14)*(n+15)*n*a(n) - (n+15)*(n+14)*(n+13)*(n+12)*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)*a(n+2) - 2*(n+15)*(n+14)*(n+13)*(n+12)*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*a(n+3) - 2*(n+15)*(n+14)*(n+13)*(n+12)*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+4)*a(n+4) + 2*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+5) + 3*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+6) + 4*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+7) - 4*(n+11)*(n+10)*(n+9)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+9) - (n+15)*(n+14)*(n+13)*(n+12)*(n+11)*(3*n+20)*a(n+10) - (2*n+11)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+11) + 2*(n+19)*(n+15)*(n+14)*(n+13)*a(n+12) + 2*(n+15)*(n+14)*(n+17)*a(n+13) + (n+18)*(n+15)*a(n+14) + a(n+15). - Robert Israel, Mar 12 2020
a(n) ~ exp(-68413/92160 + 295*n^(1/5) / (192*6^(4/5)) + 15*3^(2/5)*n^(2/5) / (32*2^(3/5)) + 5*n^(3/5) / (4*6^(2/5)) + 5*n^(4/5) / (4*6^(1/5)) - n) * n^(n - 1/10) / (sqrt(5) * 6^(1/10)) * (1 + 18025/(18432*6^(1/5)*n^(1/5))). - Vaclav Kotesovec, Dec 02 2021
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Exp[1/((1-x)(1-x^2)(1-x^3)(1-x^4))-1], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 08 2019 *)
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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-x^4))-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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