A322406 a(n) = n + n*n^n.

2, 10, 84, 1028, 15630, 279942, 5764808, 134217736, 3486784410, 100000000010, 3138428376732, 106993205379084, 3937376385699302, 155568095557812238, 6568408355712890640, 295147905179352825872, 14063084452067724991026, 708235345355337676357650, 37589973457545958193355620

Offset: 1

Author

Ivan Stoykov, Dec 07 2018

Keywords

• nonn
• easy

Comments

All terms are produced by successively applying the three basic operations: exponentiation, multiplication and addition.

Examples

			a(3) = 3 + 3*3^3 = 3 + 3*27 = 8 + 81 = 84.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..380
• R. L. Goodstein, Transfinite Ordinals in Recursive Number Theory, Journal of Symbolic Logic, Vol. 12, No. 4 (Dec. 1947), pp. 123-129.

Crossrefs

Cf. A066068, A055897.

Equals 2 * A108398.

Programs

GAP

List([1..20],n->n+n*n^n); # Muniru A Asiru, Dec 07 2018

Maple

[n+n*n^n$n=1..20]; # Muniru A Asiru, Dec 07 2018

Mathematica

a[n_]:=n+n*n^n; Array[a, 20] (* Stefano Spezia, Dec 07 2018 *)

PARI

a(n) = n+n*n^n \\ Felix Fröhlich, Dec 07 2018

Formula

E.g.f.: exp(x) * x - LambertW(-x)/(1 + LambertW(-x))^3. - Vaclav Kotesovec, Dec 20 2018

Extensions

a(12)-a(19) from Stefano Spezia, Dec 07 2018