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A368323
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Expansion of e.g.f. exp(3*x) / (4 - 3*exp(x)).
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2
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1, 6, 48, 516, 7212, 125436, 2616348, 63662556, 1770359772, 55384885596, 1925211581148, 73613650011996, 3070625126631132, 138757783222353756, 6752624341715261148, 352087859568330751836, 19582053567267458627292, 1157162515572965014445916
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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) = 3^n + 3 * Sum_{k=1..n} binomial(n,k) * a(n-k).
a(n) = (64/27)*A032033(n) - (1/3)*(2^n + 4/3 + (16/9)*0^n).
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PROG
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(PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));
a(n, m=3, t=3) = my(u=1+1/t); u^m*b(n, t)-(1/t)*sum(j=0, m-1, u^j*(m-1-j)^n);
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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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