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A338044
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E.g.f.: Sum_{j>=0} 2^j * (1 - exp(-j*x))^j.
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2
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1, 2, 30, 1106, 75870, 8355602, 1349011230, 300225115346, 88096432294110, 32956583516814482, 15309575613991708830, 8646194423981547656786, 5834064910665307876000350, 4635347672272868599469126162, 4283458291212292843946379302430
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n} (-1)^(n-j) * 2^j * j^n * j! * Stirling2(n,j).
a(n) ~ c * d^n * n!^2 / sqrt(n), where d = 4.888902442941545347850916031937657541653741222401134656609725875258275714... and c = 0.4779849579705948535026794982366398948961135521828033628215401277586...
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MATHEMATICA
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nmax = 20; CoefficientList[Series[1 + Sum[2^j*(1 - Exp[-j*x])^j, {j, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
Table[Sum[(-1)^(n-j) * 2^j * j^n * j! * StirlingS2[n, j], {j, 0, n}], {n, 1, 20}]
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PROG
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(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*2^k*k^n*k!*stirling(n, k, 2)); \\ Seiichi Manyama, Jan 31 2022
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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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