A347274 a(n) = Sum_{j=1..n} j*n^(n+1-j).

1, 8, 54, 448, 4875, 67176, 1120924, 21913088, 490329045, 12345679000, 345227121426, 10610896401216, 355457590375615, 12887297856860168, 502684312937211000, 20988295479420645376, 933876701895122362665, 44111544001370512714296, 2204350295349917301462190

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = (n^n - n)*(n/(n-1))^2 for n > 1, a(1) = 1.

a(n) = n * A062805(n) = n^2 * A058128(n) = n^3 * A060073(n).

Example

a(1) = 1;
a(2) = 2^2 + 2*2^1 = 8;
a(3) = 3^3 + 2*3^2 + 3*3^1 = 54;
a(4) = 4^4 + 2*4^3 + 3*4^2 + 4*4^1 = 448;
a(5) = 5^5 + 2*5^4 + 3*5^3 + 4*5^2 + 5*5^1 = 4875.

Maple

a:= n-> `if`(n=1, 1, (n^n-n)*(n/(n-1))^2):
seq(a(n), n=1..20);  # Alois P. Heinz, Sep 02 2021

Prog

(Python)
def A347274(n): return 1 if n == 1 else n**2*(n**n-n)//(n - 1)**2 # Chai Wah Wu, Sep 12 2021

Crossrefs

Cf. A058128, A060073, A062805.

Sequence in context: A263885 A002775 A079754 * A298985 A142703 A138403

Adjacent sequences: A347271 A347272 A347273 * A347275 A347276 A347277

Keyword

nonn

Author

Ryan Stubbs, Aug 25 2021

Status

approved