A341575 E.g.f.: log(1 - log(1 - x))^2 / 2.

1, 0, 4, 5, 58, 217, 2035, 13470, 134164, 1243770, 14129410, 164244808, 2151576620, 29671566836, 444758323628, 7055358559376, 119546765395744, 2139179551573104, 40486788832168944, 805969129348431936, 16860672502118423136, 369459637224850523808, 8467140450141232328160

Offset

2,3

Links

Table of n, a(n) for n=2..24.

Formula

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

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

Mathematica

nmax = 24; 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, 24}]

Crossrefs

Cf. A000254, A000558, A008275, A079642, A081048, A089064, A302547, A302548, A341587.

Sequence in context: A041941 A220534 A368018 * A013331 A226145 A042425

Adjacent sequences: A341572 A341573 A341574 * A341576 A341577 A341578

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 15 2021

Status

approved