Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Sep 25 2024 15:06:31
%S 1,4,43,847,23881,870721,38894653,2055873037,125480383153,
%T 8684069883409,671922832985941,57475677232902589,5385592533714824521,
%U 548596467532888667257,60358911366712739334541,7133453715771227363127301,901261693601873814393568993
%N a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 3^k * k^k.
%H Robert Israel, <a href="/A277456/b277456.txt">Table of n, a(n) for n = 0..333</a>
%F E.g.f.: exp(x)/(1+LambertW(-3*x)).
%F a(n) ~ exp(exp(-1)/3) * 3^n * n^n.
%p f:= n -> 1 + add(binomial(n,k)*3^k*k^k,k=1..n):
%p map(f, [$0..20]); # _Robert Israel_, Oct 30 2016
%t Table[1 + Sum[Binomial[n, k]*3^k*k^k, {k, 1, n}], {n, 0, 20}]
%t CoefficientList[Series[E^x/(1+LambertW[-3*x]), {x, 0, 20}], x] * Range[0, 20]!
%o (PARI) a(n) = 1 + sum(k=1, n, binomial(n,k) * 3^k * k^k); \\ _Michel Marcus_, Oct 30 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(x)/(1+lambertw(-3*x)))) \\ _G. C. Greubel_, Sep 09 2018
%o (Magma) [1] cat [1 + (&+[Binomial(n,k)*3^k*k^k: k in [1..n]]): n in [1..20]]; // _G. C. Greubel_, Sep 09 2018
%Y Cf. A086331, A277454.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Oct 16 2016