A367553 a(n) = Sum_{d|n} (d+n/d)^n.

2, 18, 128, 1506, 15552, 266548, 4194304, 89452674, 2010077696, 52439799700, 1486016741376, 46761291772836, 1587429546508288, 58431605635691172, 2305913377957871616, 97342665226310447618, 4371823119477393063936, 208266120619720061526886

Offset: 1

Author

Seiichi Manyama, Nov 22 2023

Keywords

• nonn

Comments

a(n) is even.

Crossrefs

Cf. A074400.

Programs

PARI

a(n) = sumdiv(n, d, (d+n/d)^n);

Formula

a(n) = Sum_{k=0..n} n^(n-k) * binomial(n,k) * (Sum_{d|n} d^(2*k-n)) = Sum_{k=0..n} binomial(n,k) * (Sum_{d|n} d^k * (n/d)^(n-k)).