A356127 a(n) = Sum_{k=1..n} k^k * binomial(floor(n/k)+1,2).

1, 7, 37, 305, 3435, 50163, 873713, 17651465, 405072044, 10405078324, 295716748946, 9211817291426, 312086923883692, 11424093751088836, 449317984131957736, 18896062057875064856, 846136323944211829050, 40192544399241524385636

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = Sum_{k=1..n} k * Sum_{d|k} d^(d-1).

G.f.: (1/(1-x)) * Sum_{k>=1} (k * x)^k/(1 - x^k)^2.

Mathematica

a[n_] := Sum[k^k * Binomial[Floor[n/k] + 1, 2], {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Jul 28 2022*)

Prog

(PARI) a(n) = sum(k=1, n, k^k*binomial(n\k+1, 2));
(PARI) a(n) = sum(k=1, n, k*sumdiv(k, d, d^(d-1)));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-x^k)^2)/(1-x))

Crossrefs

Cf. A355887, A355950.

Sequence in context: A199192 A089677 A075996 * A343568 A173766 A093168

Adjacent sequences: A356124 A356125 A356126 * A356128 A356129 A356130

Keyword

nonn

Author

Seiichi Manyama, Jul 27 2022

Status

approved