A349970 a(n) = Sum_{k=0..n} (2*k)^(n-k).

1, 1, 3, 9, 31, 125, 579, 3009, 17255, 108005, 731883, 5331625, 41501135, 343405709, 3007557523, 27775308049, 269603741111, 2742598070709, 29164361115067, 323444222468089, 3733412864370975, 44767318872513885, 556707323098632547, 7168524182698345313

Offset: 0

Author

Seiichi Manyama, Dec 07 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A349963, A349969.

Programs

Mathematica

a[n_] := Sum[If[k == n == 0, 1, (2*k)^(n - k)], {k, 0, n}]; Array[a, 24, 0] (* Amiram Eldar, Dec 07 2021 *)

PARI

a(n) = sum(k=0, n, (2*k)^(n-k));

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-2*k*x)))

Formula

G.f.: Sum_{k>=0} x^k/(1 - 2*k * x).

a(n) ~ sqrt(Pi) * (2*n/LambertW(2*exp(1)*n))^(1/2 + n - n/LambertW(2*exp(1)*n)) / sqrt(1 + LambertW(2*exp(1)*n)). - Vaclav Kotesovec, Dec 07 2021