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A293050
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E.g.f.: exp(x^4/(1 - x)).
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4
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1, 0, 0, 0, 24, 120, 720, 5040, 60480, 725760, 9072000, 119750400, 1756339200, 28021593600, 479480601600, 8717829120000, 168254102016000, 3438311804928000, 74160828758016000, 1682757222322176000, 40061786401308672000, 998402161605488640000
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history;
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internal format)
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OFFSET
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0,5
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LINKS
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FORMULA
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E.g.f.: Product_{i>3} exp(x^i).
a(n) = 2*(n-1)*a(n-1) - (n-2)*(n-1)*a(n-2) + 4*(n-3)*(n-2)*(n-1)*a(n-4) - 3*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5).
a(n) ~ n^(n-1/4) * exp(-7/2 + 2*sqrt(n) - n) / sqrt(2).
(End)
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-j)*binomial(n-1, j-1)*j!, j=4..n))
end:
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MATHEMATICA
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a[n_] := a[n] = If[n==0, 1, Sum[a[n-j] Binomial[n-1, j-1] j!, {j, 4, n}]];
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PROG
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(PARI) x='x+O('x^66); Vec(serlaplace(exp(x^4/(1-x))))
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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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