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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..375

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...

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}]

Crossrefs

Cf. A277409, A226572.

Sequence in context: A180623 A128329 A211828 * A006149 A207833 A121413

Adjacent sequences: A277756 A277757 A277758 * A277760 A277761 A277762

Keyword

nonn

Author

Vaclav Kotesovec, Oct 30 2016

Status

approved