A341588 E.g.f.: -log(1 + log(1 - x))^3 / 6.

1, 12, 130, 1485, 18508, 253400, 3805723, 62437500, 1113510409, 21479997957, 446094038806, 9930796412082, 236037249893092, 5968192832899412, 160007282538148508, 4534905316824903144, 135500246340709682692, 4257646241716404353684, 140366073694357927723936, 4845119946789226304526392

Offset

3,2

Links

Seiichi Manyama, Table of n, a(n) for n = 3..418

Formula

a(n) = Sum_{k=3..n} |Stirling1(n, k) * Stirling1(k, 3)|.

a(n) ~ (n-1)! * log(n)^2 / (2 * (1 - exp(-1))^n) * (1 + (2*gamma - 2*log(exp(1) - 1)) / log(n) + (gamma^2 - Pi^2/6 - 2*log(exp(1) - 1)*gamma + log(exp(1)-1)^2) / log(n)^2). - Vaclav Kotesovec, Jun 04 2022

Mathematica

nmax = 22; CoefficientList[Series[-Log[1 + Log[1 - x]]^3/6, {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 3] &
Table[Sum[Abs[StirlingS1[n, k] StirlingS1[k, 3]], {k, 3, n}], {n, 3, 22}]

Crossrefs

Cf. A000399, A000559, A003713, A008275, A039814, A341587.

Sequence in context: A163414 A111777 A209013 * A240798 A160962 A097783

Adjacent sequences: A341585 A341586 A341587 * A341589 A341590 A341591

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 15 2021

Status

approved