A341587 E.g.f.: log(1 + log(1 - x))^2 / 2.

1, 6, 40, 315, 2908, 30989, 375611, 5112570, 77305024, 1286640410, 23387713930, 461187042992, 9808283703684, 223833267479764, 5456669750439788, 141540592345674800, 3892707724320135616, 113153294901088030320, 3466501398608272647984, 111636571036702743967104, 3770483138507706753943584

Offset

2,2

Links

Seiichi Manyama, Table of n, a(n) for n = 2..418

Formula

a(n) = Sum_{k=2..n} |Stirling1(n, k) * Stirling1(k, 2)|.

a(n) = Sum_{k=2..n} |Stirling1(n, k)| * (k-1)! * H(k-1), where H(k) is the k-th harmonic number.

a(n) = Sum_{k=1..n-1} binomial(n-1, k) * A003713(k) * A003713(n-k).

a(n) = A052822(n) / 2.

a(n) ~ sqrt(2*Pi) * log(n) * n^(n - 1/2) / (exp(1) - 1)^n * (1 + (gamma - log(exp(1) - 1))/log(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Feb 15 2021

Mathematica

nmax = 22; CoefficientList[Series[Log[1 + Log[1 - x]]^2/2, {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 2] &
Table[Sum[Abs[StirlingS1[n, k] StirlingS1[k, 2]], {k, 2, n}], {n, 2, 22}]

Crossrefs

Cf. A000254, A000558, A003713, A008275, A039814, A052822, A302547, A302548, A341588.

Sequence in context: A083805 A181571 A231126 * A006387 A014481 A184266

Adjacent sequences: A341584 A341585 A341586 * A341588 A341589 A341590

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 15 2021

Status

approved