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 A371768 #10 Apr 09 2024 10:44:33 %S A371768 0,2,6,34,220,1868,18648,222696,3061728,48199392,852857280, %T A371768 16813212480,365177928960,8671294183680,223409173317120, %U A371768 6207795845798400,185021865565286400,5887763630809804800,199220359130518118400,7141874528908565913600,270391380094261923840000 %N A371768 a(n) = n! * [x^n] (log(2*x - 1) - log(x - 1) - log(x + 1)) / (x - 1). Row sums of A371685. %p A371768 assume(x > 0): egf := (log(2*x - 1) - log(x - 1) - log(x + 1))/(x - 1): %p A371768 ser := series(egf, x, 24): seq(n!*coeff(ser, x, n), n = 0..20); %p A371768 # Recurrence: %p A371768 a := proc(n) option remember; if n < 4 then return [0, 2, 6, 34][n+1] fi; %p A371768 (2*(n-4)^4 + 14*(n-4)^3 + 34*(n-4)^2 + 34*n - 124)*a(n-4) - (3*(n-4)^3 + 19*(n-4)^2 + 38*n - 128)*a(n-3) - ((n-4)^2 + 7*n - 16)*a(n-2) + (3*n - 2)*a(n-1) end: %p A371768 seq(a(n), n = 0..20); %Y A371768 Cf. A371685. %K A371768 nonn %O A371768 0,2 %A A371768 _Peter Luschny_, Apr 09 2024