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
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.
Programs
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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.
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
Comments