A258388 a(n) = n^(n+1) + (n-1)^n.

1, 1, 9, 89, 1105, 16649, 295561, 6044737, 139982529, 3621002129, 103486784401, 3238428376721, 110131633755793, 4044369591078361, 159505471943511513, 6723976451270702849, 301716313535065716481, 14358232357247077816865, 722298429807405401348641

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..350 (first 20 terms from Daniel Suteu)

Formula

From Robert Israel, Jun 04 2015: (Start)

a(n) = A007778(n-1) + A007778(n) for n>0.

E.g.f.: 1/(1 + W(-x))^3 - 1/(1 + W(-x))^2 - x/(W(-x)*(1+W(-x))) where W is the Lambert W function. (End)

Example

a(3) = 3^(3+1) + (3-1)^3 = 3^4 + 2^3 = 81 + 8 = 89.

Maple

a:= n-> n^(n+1)+(n-1)^n:
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 04 2015

Mathematica

Array[#^(# + 1) + (# - 1)^# &, 20] (* Vincenzo Librandi, May 29 2015 *)

Prog

(Sidef)
func a(n) {
    (n-1)**n + n**(n+1)
};
1.to(Math.inf).each { |n|
    say a(n);
};
(Magma) [n^(n+1)+(n-1)^n: n in [0..20]]; // Vincenzo Librandi, May 29 2015
(PARI) vector(10, n, n^(n+1)+(n-1)^n) \\ Derek Orr, Jun 01 2015

Crossrefs

Cf. A007778, A084363.

Sequence in context: A101679 A075507 A094935 * A296618 A230114 A187090

Adjacent sequences: A258385 A258386 A258387 * A258389 A258390 A258391

Keyword

nonn,easy

Author

Daniel Suteu, May 28 2015

Status

approved