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A277456 a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 3^k * k^k. 6
1, 4, 43, 847, 23881, 870721, 38894653, 2055873037, 125480383153, 8684069883409, 671922832985941, 57475677232902589, 5385592533714824521, 548596467532888667257, 60358911366712739334541, 7133453715771227363127301, 901261693601873814393568993 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..333

FORMULA

E.g.f.: exp(x)/(1+LambertW(-3*x)).

a(n) ~ exp(exp(-1)/3) * 3^n * n^n.

MAPLE

f:= n -> 1 + add(binomial(n, k)*3^k*k^k, k=1..n):

map(f, [$0..20]); # Robert Israel, Oct 30 2016

MATHEMATICA

Table[1 + Sum[Binomial[n, k]*3^k*k^k, {k, 1, n}], {n, 0, 20}]

CoefficientList[Series[E^x/(1+LambertW[-3*x]), {x, 0, 20}], x] * Range[0, 20]!

PROG

(PARI) a(n) = 1 + sum(k=1, n, binomial(n, k) * 3^k * k^k); \\ Michel Marcus, Oct 30 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(x)/(1+lambertw(-3*x)))) \\ G. C. Greubel, Sep 09 2018

(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

CROSSREFS

Cf. A086331, A277454.

Sequence in context: A326432 A074702 A197717 * A317140 A152282 A153255

Adjacent sequences: A277453 A277454 A277455 * A277457 A277458 A277459

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 16 2016

STATUS

approved

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)