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.
%I A061302 #21 Feb 10 2023 17:53:51
%S A061302 0,2,6,36,320,3750,54432,941192,18874368,430467210,11000000000,
%T A061302 311249095212,9659108818944,326173191714734,11905721598812160,
%U A061302 467086816406250000,19599665578316398592,875901453762003632658
%N A061302 a(n) = n! * [x^n] W(-x)*(W(-x) + 2)/(W(-x) + 1), where W denotes Lambert's W function.
%D A061302 Stephan Wolfram, The Mathematica Book, 4th Edition, Cambridge University Press, section 3.2.10 'Special Functions', page 772, 1999.
%F A061302 a(n) = (n+1)*n^(n-1) with a(0) = 0.
%e A061302 2*x + 6*x^2 +36*x^3 + 320*x^4 + 3750*x^5 + 54432*x^6 + 941192*x^7 + ...
%p A061302 W := LambertW: egf := -W(-x)*(W(-x) + 2)/(W(-x) + 1):
%p A061302 ser := series(egf, x, 20): seq(n!*coeff(ser, x, n), n = 0..17); # _Peter Luschny_, Feb 10 2023
%t A061302 Range[18]!CoefficientList[ Series[ -ProductLog[ -x], {x, 0, 17}], x] (* _Robert G. Wilson v_, Mar 23 2005 *)
%t A061302 a[ n_] := If[ n < 0, 0, (n + 1)! SeriesCoefficient[ -ProductLog[-x], {x, 0, n}]] (* _Michael Somos_, Jun 07 2012 *)
%Y A061302 Cf. A061250.
%Y A061302 Essentially the same as A055541.
%K A061302 nonn,easy
%O A061302 0,2
%A A061302 Gero Burghardt (gerogoestohollywood(AT)yahoo.de), Jun 05 2001
%E A061302 Corrected and extended by _Jason Earls_, Jun 09 2001
%E A061302 Name made consistent with offset by _Peter Luschny_, Feb 10 2023