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A358064
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Expansion of e.g.f. 1/(1 - x * exp(x^2)).
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8
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1, 1, 2, 12, 72, 540, 5040, 53760, 658560, 9087120, 139104000, 2343781440, 43078210560, 857676980160, 18390744852480, 422504399116800, 10353592759910400, 269576216304595200, 7431814422621388800, 216266552026593868800, 6624610236968435712000
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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) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/k!.
a(n) ~ n! * 2^(n/2) / ((1 + LambertW(2)) * LambertW(2)^(n/2)). - Vaclav Kotesovec, Nov 01 2022
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[1/(1-x Exp[x^2]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 14 2024 *)
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^2))))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/k!);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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