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A306495
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Expansion of e.g.f. (2-exp(-x))*exp(x)/(x-1)^2.
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2
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1, 4, 16, 74, 402, 2542, 18446, 151482, 1390738, 14126582, 157365222, 1908110866, 25022451482, 352918443438, 5327630246542, 85716034274282, 1464281837606946, 26470821156031462, 504879319309407158, 10132393298394712002, 213441590598213760042
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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_{k=-n..n} A324224(n+1,k).
a(n) = (2*n+1)*a(n-1) - (n+2)*(n-1)*a(n-2) + (n-1)*(n-2)*a(n-3) for n > 2, a(n) = 4^n for n < 3.
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MAPLE
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egf:= (2-exp(-x))*exp(x)/(x-1)^2:
a:= n-> n! * coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..23);
# second Maple program:
a:= proc(n) option remember; `if`(n<3, 4^n,
(2*n+1)*a(n-1)-(n+2)*(n-1)*a(n-2)+(n-1)*(n-2)*a(n-3))
end:
seq(a(n), n=0..23);
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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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