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A365794
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Expansion of e.g.f. 1 / (3 - 2 * exp(2*x))^(3/4).
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2
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1, 3, 27, 369, 6849, 160803, 4566987, 152204769, 5822610849, 251445000483, 12098060349147, 641736701136369, 37204969609266849, 2340437711290748163, 158770522442243864907, 11553653430580844747169, 897732793887437892390849, 74182365989862425679675843
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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=0..n} 2^(n-k) * (Product_{j=0..k-1} (4*j+3)) * Stirling2(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} 2^k * (2 - 1/2 * k/n) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 3*a(n-1) - 3*Sum_{k=1..n-1} (-2)^k * binomial(n-1,k) * a(n-k).
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PROG
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(PARI) a(n) = sum(k=0, n, 2^(n-k)*prod(j=0, k-1, 4*j+3)*stirling(n, k, 2));
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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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