A112999 - OEIS

%I #29 Nov 30 2020 03:59:10

%S 1,5,221,331997,24883531997,139314094387531997,

%T 82606411393217618227531997,6984964247224120535022357995827531997,

%U 109110688415578301444592123476429107940843827531997

%N Partial sums of A036740.

%H Seiichi Manyama, <a href="/A112999/b112999.txt">Table of n, a(n) for n = 1..30</a>

%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://primes.utm.edu/curios/page.php/331997.html">Prime Curios! 331997</a>

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

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

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

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

%e a(1) = (1!)^1 = 1^1 = 1.

%e a(2) = (1!)^1 + (2!)^2 = 1^1 + 2^2 = 1 + 4 = 5.

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

%t Table[Sum[Product[m^k,{m,1,k}],{k,1,n}],{n,1,10}] (* _Vaclav Kotesovec_, Nov 01 2014 *)

%t Accumulate[Table[(n!)^n,{n,10}]] (* _Harvey P. Dale_, Dec 23 2019 *)

%o (PARI) a(n) = sum(k=1, n, k!^k); \\ _Michel Marcus_, Nov 30 2020

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

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Jan 03 2006