A338448 E.g.f.: 1 / (1 - x - log(1 - x)).

1, 0, -1, -2, 0, 16, 50, -132, -2184, -9984, 6912, 341760, 38544, -47086272, -702019344, -6076389984, -43980940800, -656377887744, -16782743357568, -368775477229824, -6770025717901056, -118247220867640320, -2271088046291742720, -50203882870716579840

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = -Sum_{k=2..n} binomial(n,k) * (k-1)! * a(n-k).

a(n) ~ -n! / (n * log(n)^2) * (1 - 2*gamma/log(n) + (3*gamma^2 - Pi^2/2)/log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 29 2020

Mathematica

nmax = 23; CoefficientList[Series[1/(1 - x - Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] (k - 1)! a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 23}]

Prog

(PARI) my(x='x + O('x^30)); Vec(serlaplace(1/(1 - x - log(1 - x)))) \\ Michel Marcus, Oct 29 2020

Crossrefs

Cf. A006252, A089148, A226226.

Sequence in context: A009266 A009246 A358629 * A012414 A098336 A116093

Adjacent sequences: A338445 A338446 A338447 * A338449 A338450 A338451

Keyword

sign

Author

Ilya Gutkovskiy, Oct 28 2020

Status

approved