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A358080
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Expansion of e.g.f. 1/(1 - x^2 * exp(x)).
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4
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1, 0, 2, 6, 36, 260, 2190, 21882, 248696, 3181320, 45229050, 707208590, 12063902532, 222939837276, 4436813677478, 94605994108290, 2151763873634160, 51999544476324752, 1330540380342907506, 35936656483848501654, 1021700660649312689660
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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)} k^(n - 2*k)/(n - 2*k)!.
a(n) ~ n! / ((1 + LambertW(1/2)) * 2^(n+1) * LambertW(1/2)^n). - Vaclav Kotesovec, Oct 30 2022
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^2*exp(x))))
(PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)/(n-2*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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