A368524 a(n) = Sum_{k=1..n} k^2 * n^(n-k).

0, 1, 6, 30, 180, 1455, 15666, 213500, 3521736, 68101245, 1508916310, 37661140506, 1045012524348, 31900040161899, 1062139933257690, 38299757176168440, 1486670929792295696, 61800664096000744569, 2738952078516469743678, 128909373997071187219990

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = [x^n] x * (1+x)/((1-n*x) * (1-x)^3).

a(n) = n * (n+1) * (n^n - n^2 + n - 1)/(n-1)^3 for n > 1.

Prog

(PARI) a(n) = sum(k=1, n, k^2*n^(n-k));

Crossrefs

Cf. A062805, A368505, A368525.

Cf. A368526, A368534.

Sequence in context: A063888 A029571 A357599 * A259276 A109501 A239488

Adjacent sequences: A368521 A368522 A368523 * A368525 A368526 A368527

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 28 2023

Status

approved