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A294119
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Expansion of e.g.f.: exp(2*((1+x)^2 - 1)).
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3
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1, 4, 20, 112, 688, 4544, 31936, 236800, 1841408, 14943232, 126063616, 1101983744, 9954734080, 92714156032, 888502796288, 8746003922944, 88294183469056, 912920984944640, 9655688415674368, 104353064578711552, 1151244577906098176, 12953223477921316864
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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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E.g.f.: exp(2*((1+x)^2 - 1)).
a(n) ~ 2^(n - 1/2) * n^(n/2) * exp(-1 + 2*sqrt(n) - n/2). - Vaclav Kotesovec, Oct 23 2017
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MAPLE
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f:= rectoproc({a(n)=4*a(n-1)+4*(n-1)*a(n-2), a(0)=1, a(1)=4}, a(n), remember):
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MATHEMATICA
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nmax = 20; CoefficientList[Series[E^(2*((1+x)^2 - 1)), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 23 2017 *)
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(2*((1+x)^2-1))))
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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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