cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A338448 #9 Oct 30 2020 02:32:32
%S A338448 1,0,-1,-2,0,16,50,-132,-2184,-9984,6912,341760,38544,-47086272,
%T A338448 -702019344,-6076389984,-43980940800,-656377887744,-16782743357568,
%U A338448 -368775477229824,-6770025717901056,-118247220867640320,-2271088046291742720,-50203882870716579840
%N A338448 E.g.f.: 1 / (1 - x - log(1 - x)).
%F A338448 a(0) = 1; a(n) = -Sum_{k=2..n} binomial(n,k) * (k-1)! * a(n-k).
%F A338448 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
%t A338448 nmax = 23; CoefficientList[Series[1/(1 - x - Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A338448 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}]
%o A338448 (PARI) my(x='x + O('x^30)); Vec(serlaplace(1/(1 - x - log(1 - x)))) \\ _Michel Marcus_, Oct 29 2020
%Y A338448 Cf. A006252, A089148, A226226.
%K A338448 sign
%O A338448 0,4
%A A338448 _Ilya Gutkovskiy_, Oct 28 2020