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A272230
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E.g.f.: 2*exp(x)/(exp(2*x)+1+2*x).
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1
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1, -1, 3, -15, 93, -725, 6815, -74627, 933849, -13148361, 205690779, -3539545559, 66446203637, -1351309774685, 29595401433975, -694475294514315, 17382734374217265, -462283425487469585, 13017336622169166515, -386916316537712637215, 12105656546432789499405, -397693919494074869853285
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OFFSET
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0,3
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COMMENTS
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Empirically, for odd n, n|a(n) and for even n, (n-1)|a(n).
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LINKS
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FORMULA
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a(n) = 1-2n*a(n-1)-Sum_{k=0..n-2}binomial(n,k)*2^(n-k-1)*a(k)
a(n) = Sum_{k=0..n} Sum_{j=0..k} Sum_{i=0..n} binomial(n,k)*binomial(k+i,i)*binomial(n,i)(i!*(-1)^(i+j)*(2j+1)^(n-i))/(2^k)
a(n) ~ n! * (-1)^n*sqrt(LambertW(exp(-1)))*2^(n+1) / (1+LambertW(exp(-1)))^(n+2). - Vaclav Kotesovec, May 03 2016
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MAPLE
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S:= series(2*exp(x)/(exp(2*x)+1+2*x), x, 31):
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MATHEMATICA
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a[n_]:=Sum[Sum[Sum[Binomial[k, j]*Binomial[k + i, i]*Binomial[n, i]*((i!*(-1)^(i + j)*(2 j + 1)^(n - i))/(2^k)), {i, 0, n}], {j, 0, k}], {k, 0, n}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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