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

1, 1, 23, 1836, 361754, 143195025, 99986786773, 112625837135056, 191736660977760804, 469456525723134676365, 1589874326596159958849175, 7216642860485686755145923828, 42781019992428263086709058587150, 324097110833947198922869762652717041

Offset: 0

Author

Ilya Gutkovskiy, Sep 21 2018

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..167

Crossrefs

Main diagonal of A320253.

Cf. A000670, A004700, A004701, A004702, A004703, A004704, A004705, A004706, A004707, A004708, A319509.

Programs

Mathematica

Table[n! SeriesCoefficient[1/(1 + n - Exp[x] (Exp[n x] - 1)/(Exp[x] - 1)), {x, 0, n}], {n, 0, 13}]

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)};
for(n=0, 15, print1(a(n), ", ")) \\ G. C. Greubel, Oct 09 2018

Formula

a(n) = n! * [x^n] 1/(1 + n - exp(x) - exp(2*x) - exp(3*x) - ... - exp(n*x)).

a(n) ~ sqrt(2*Pi) * n^(3*n + 1/2) / (2^n * exp(n - 5/3)). - Vaclav Kotesovec, Oct 09 2018