A375730 a(n) = n^n + n*n + n+n + 1.

2, 5, 13, 43, 281, 3161, 46705, 823607, 16777297, 387420589, 10000000121, 285311670755, 8916100448425, 302875106592449, 11112006825558241, 437893890380859631, 18446744073709551905, 827240261886336764501, 39346408075296537575785, 1978419655660313589124379

Offset: 0

Author

Anthony Veglia, Aug 25 2024

Keywords

• nonn
• easy

Comments

The sum of "n OP n" for hyper-operators 0 to 3, where 0 = succession, 1 = addition, 2 = multiplication, 3 = exponentiation.

Examples

			a(0) = (0^0)+(0*0)+(0+0)+1 = 1+0+0+1 = 2.
a(3) = (3^3)+(3*3)+(3+3)+1 = 27+9+6+1 = 43.
		

Crossrefs

Cf. A000012, A000290, A000312, A005843, A189896.

Programs

Mathematica

Join[{2},Table[n^n+(n+1)^2,{n,19}]] (* James C. McMahon, Sep 13 2024 *)

Python

def A375730(n): return n*(n*(n**(n-2)+1)+2)+1 if n>1 else 3*n+2 # Chai Wah Wu, Sep 02 2024

Formula

a(n) = n^n + (n+1)^2.

a(n) = A000312(n) + A000290(n) + A005843(n) + A000012(n).

E.g.f.: (1+3*x+x^2)*exp(x)+1/(1+LambertW(-x)). - Alois P. Heinz, Aug 26 2024

Extensions

a(19) corrected by James C. McMahon, Sep 13 2024