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