cp's OEIS Frontend

A319508 a(n) = n! * [x^n] 1/(1 + n - exp(x)*(exp(n*x) - 1)/(exp(x) - 1)).

%I A319508 #16 Oct 12 2018 03:05:15
%S A319508 1,1,23,1836,361754,143195025,99986786773,112625837135056,
%T A319508 191736660977760804,469456525723134676365,1589874326596159958849175,
%U A319508 7216642860485686755145923828,42781019992428263086709058587150,324097110833947198922869762652717041
%N A319508 a(n) = n! * [x^n] 1/(1 + n - exp(x)*(exp(n*x) - 1)/(exp(x) - 1)).
%H A319508 G. C. Greubel, <a href="/A319508/b319508.txt">Table of n, a(n) for n = 0..167</a>
%F A319508 a(n) = n! * [x^n] 1/(1 + n - exp(x) - exp(2*x) - exp(3*x) - ... - exp(n*x)).
%F A319508 a(n) ~ sqrt(2*Pi) * n^(3*n + 1/2) / (2^n * exp(n - 5/3)). - _Vaclav Kotesovec_, Oct 09 2018
%t A319508 Table[n! SeriesCoefficient[1/(1 + n - Exp[x] (Exp[n x] - 1)/(Exp[x] - 1)), {x, 0, n}], {n, 0, 13}]
%o A319508 (PARI) default(seriesprecision, 101); {a(n) = n!*polcoeff((1/(1+n-exp(x)*(exp(n*x)-1)/(exp(x)-1)) + O(x^(n+1))), n)};
%o A319508 for(n=0, 15, print1(a(n), ", ")) \\ _G. C. Greubel_, Oct 09 2018
%Y A319508 Main diagonal of A320253.
%Y A319508 Cf. A000670, A004700, A004701, A004702, A004703, A004704, A004705, A004706, A004707, A004708, A319509.
%K A319508 nonn
%O A319508 0,3
%A A319508 _Ilya Gutkovskiy_, Sep 21 2018