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A367883
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Expansion of e.g.f. 1/(1 + x * log(1-2*x)).
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2
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1, 0, 4, 12, 160, 1440, 20928, 309120, 5604352, 110896128, 2480762880, 60669480960, 1625897189376, 47158671605760, 1475038408015872, 49434699759943680, 1768135111433256960, 67206058595340779520, 2705431746964327759872
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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} 2^(k-1)/(k-1) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-k) * k! * |Stirling1(n-k,k)|/(n-k)!.
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[1/(1+x Log[1-2x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 11 2024 *)
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PROG
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(PARI) a(n) = n!*sum(k=0, n\2, 2^(n-k)*k!*abs(stirling(n-k, k, 1))/(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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