A393792 Expansion of e.g.f. -log(1 - x) / (2 - exp(x)).

0, 1, 3, 14, 84, 619, 5425, 55194, 639912, 8332083, 120417733, 1913110462, 33143888888, 621897534075, 12564606277249, 271955197419546, 6278353087337264, 153994212700687003, 3999212962967490501, 109627082690360270862, 3163241912269490383088, 95836922636384815294995

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * A000670(n-k).

a(n) ~ log(1/(1-log(2))) * sqrt(Pi/2) * n^(n + 1/2) / (exp(n) * log(2)^(n+1)). - Vaclav Kotesovec, Feb 27 2026

Mathematica

nmax = 21; CoefficientList[Series[-Log[1 - x]/(2 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k] (k - 1)! (PolyLog[k - n, 1/2] + KroneckerDelta[n - k])/2, {k, 1, n}], {n, 0, 21}]

Crossrefs

Cf. A000629, A000670, A002741, A337000.

Sequence in context: A088717 A111538 A354003 * A324237 A352887 A230218

Adjacent sequences: A393789 A393790 A393791 * A393793 A393794 A393795

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 27 2026

Status

approved