A112999 Partial sums of A036740.

1, 5, 221, 331997, 24883531997, 139314094387531997, 82606411393217618227531997, 6984964247224120535022357995827531997, 109110688415578301444592123476429107940843827531997

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..30

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 331997

Formula

a(n) = Sum_{k=1..n} (k!)^k.

a(n) = Sum_{k=1..n} (A000142(k))^k.

a(n) = Sum_{k=1..n} A036740(k).

a(n) = Sum_{k=1..n} A002109(k) * A000178(k-1).

Example

a(1) = (1!)^1 = 1^1 = 1.
a(2) = (1!)^1 + (2!)^2 = 1^1 + 2^2 = 1 + 4 = 5.
a(3) = (1!)^1 + (2!)^2 + (3!)^3 = 1^1 + 2^2 + 6^3 = 1 + 4 + 216 = 221.

Mathematica

Table[Sum[Product[m^k, {m, 1, k}], {k, 1, n}], {n, 1, 10}] (* Vaclav Kotesovec, Nov 01 2014 *)
Accumulate[Table[(n!)^n, {n, 10}]] (* Harvey P. Dale, Dec 23 2019 *)

Prog

(PARI) a(n) = sum(k=1, n, k!^k); \\ Michel Marcus, Nov 30 2020

Crossrefs

Cf. A000142, A000178, A002109, A036740, A339311.

Sequence in context: A066462 A046193 A195633 * A337965 A225818 A185551

Adjacent sequences: A112996 A112997 A112998 * A113000 A113001 A113002

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 03 2006

Status

approved