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A367886
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Expansion of e.g.f. 1/(1 - x * (exp(3*x) - 1)).
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1
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1, 0, 6, 27, 324, 3645, 54918, 923643, 18061704, 394663833, 9607469130, 256997250279, 7502660832780, 237243300445125, 8079508278302958, 294800526215739315, 11473728720705019152, 474469344621574172721, 20774758472643152149650
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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(0) = 1; a(n) = n * Sum_{k=2..n} 3^(k-1) * binomial(n-1,k-1) * a(n-k).
a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-k) * k! * Stirling2(n-k,k)/(n-k)!.
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PROG
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(PARI) a(n) = n!*sum(k=0, n\2, 3^(n-k)*k!*stirling(n-k, k, 2)/(n-k)!);
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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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