A349961 a(n) = Sum_{k=0..n} (2*n)^k.

1, 3, 21, 259, 4681, 111111, 3257437, 113522235, 4581298449, 210027483919, 10778947368421, 612142982430915, 38108188628928601, 2580398988131886039, 188802050194014479853, 14843696896551724137931, 1247923426698972051309601, 111713733654631566667971615

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = ((2*n)^(n+1) - 1)/(2*n - 1).

Mathematica

a[0] = 1; a[n_] := Sum[(2*n)^k, {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Dec 07 2021 *)

Prog

(PARI) a(n) = sum(k=0, n, (2*n)^k);
(PARI) a(n) = ((2*n)^(n+1)-1)/(2*n-1);

Crossrefs

Cf. A031973, A155956.

Sequence in context: A317059 A262939 A232470 * A251573 A265002 A012131

Adjacent sequences: A349958 A349959 A349960 * A349962 A349963 A349964

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 07 2021

Status

approved