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A354147
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Expansion of e.g.f. 1/(1 - 4 * log(1+x)).
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4
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1, 4, 28, 296, 4168, 73376, 1550048, 38202048, 1076017344, 34096092672, 1200459182592, 46492497859584, 1964295942558720, 89906908894150656, 4431634108980264960, 234044235939806232576, 13184410813249253031936, 789137065405617987354624
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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(0) = 1; a(n) = 4 * Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k).
a(n) = Sum_{k=0..n} 4^k * k! * Stirling1(n, k).
a(n) ~ n! * exp(1/4) / (4 * (exp(1/4)-1)^(n+1)). - Vaclav Kotesovec, Jun 04 2022
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-4*log(1+x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=4*sum(j=1, i, (-1)^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n, 4^k*k!*stirling(n, k, 1));
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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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