# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a277456 Showing 1-1 of 1 %I A277456 #18 Sep 25 2024 15:06:31 %S A277456 1,4,43,847,23881,870721,38894653,2055873037,125480383153, %T A277456 8684069883409,671922832985941,57475677232902589,5385592533714824521, %U A277456 548596467532888667257,60358911366712739334541,7133453715771227363127301,901261693601873814393568993 %N A277456 a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 3^k * k^k. %H A277456 Robert Israel, Table of n, a(n) for n = 0..333 %F A277456 E.g.f.: exp(x)/(1+LambertW(-3*x)). %F A277456 a(n) ~ exp(exp(-1)/3) * 3^n * n^n. %p A277456 f:= n -> 1 + add(binomial(n,k)*3^k*k^k,k=1..n): %p A277456 map(f, [$0..20]); # _Robert Israel_, Oct 30 2016 %t A277456 Table[1 + Sum[Binomial[n, k]*3^k*k^k, {k, 1, n}], {n, 0, 20}] %t A277456 CoefficientList[Series[E^x/(1+LambertW[-3*x]), {x, 0, 20}], x] * Range[0, 20]! %o A277456 (PARI) a(n) = 1 + sum(k=1, n, binomial(n,k) * 3^k * k^k); \\ _Michel Marcus_, Oct 30 2016 %o A277456 (PARI) x='x+O('x^30); Vec(serlaplace(exp(x)/(1+lambertw(-3*x)))) \\ _G. C. Greubel_, Sep 09 2018 %o A277456 (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 A277456 Cf. A086331, A277454. %K A277456 nonn %O A277456 0,2 %A A277456 _Vaclav Kotesovec_, Oct 16 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE