A277759 a(n) equals the coefficient of x^n in n!*(1 - log(1-x))^n.
1, 1, 4, 30, 324, 4540, 78060, 1589448, 37388400, 997513200, 29759790240, 981669324240, 35475203063520, 1393746645107232, 59147129937893088, 2696314664384853120, 131405475202661963520, 6817779852438948837120, 375193156508083422581760
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..375
Programs
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Mathematica
Table[n!*SeriesCoefficient[(1-Log[1-x])^n, {x, 0, n}], {n, 0, 20}] Table[Sum[Binomial[n, k]*k!*(-1)^(n-k)*StirlingS1[n, k], {k, 0, n}], {n, 0, 20}]
Formula
a(n) = Sum_{k=0..n} binomial(n,k) * k! * (-1)^(n-k) * Stirling1(n,k).
a(n) ~ d^n * n^n / (sqrt(d-1) * exp(n)), where d = A226572 = -LambertW(-1, -exp(-2)) = 3.146193220620582585237...