A277759 - OEIS

%I #28 Oct 30 2016 08:44:32

%S 1,1,4,30,324,4540,78060,1589448,37388400,997513200,29759790240,

%T 981669324240,35475203063520,1393746645107232,59147129937893088,

%U 2696314664384853120,131405475202661963520,6817779852438948837120,375193156508083422581760

%N a(n) equals the coefficient of x^n in n!*(1 - log(1-x))^n.

%H Vaclav Kotesovec, <a href="/A277759/b277759.txt">Table of n, a(n) for n = 0..375</a>

%F a(n) = Sum_{k=0..n} binomial(n,k) * k! * (-1)^(n-k) * Stirling1(n,k).

%F a(n) ~ d^n * n^n / (sqrt(d-1) * exp(n)), where d = A226572 = -LambertW(-1, -exp(-2)) = 3.146193220620582585237...

%t Table[n!*SeriesCoefficient[(1-Log[1-x])^n, {x, 0, n}], {n, 0, 20}]

%t Table[Sum[Binomial[n, k]*k!*(-1)^(n-k)*StirlingS1[n, k], {k, 0, n}], {n, 0, 20}]

%Y Cf. A277409, A226572.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 30 2016