A358389 a(n) = n * Sum_{d|n} (d + n/d - 2)!/d!.

1, 3, 7, 29, 121, 745, 5041, 40425, 362917, 3629411, 39916801, 479006233, 6227020801, 87178326495, 1307674369891, 20922790211057, 355687428096001, 6402373709009185, 121645100408832001, 2432902008212933061, 51090942171709581289, 1124000727778046764823

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..449

Formula

G.f.: Sum_{k>0} k! * (x/(1 - x^k))^k.

If p is prime, a(p) = 1 + p!.

Mathematica

Table[n*DivisorSum[n, ((# + n/# - 2)!)/(#!) &], {n, 22}] (* Michael De Vlieger, Nov 13 2022 *)

Prog

(PARI) a(n) = n*sumdiv(n, d, (d+n/d-2)!/d!);
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*(x/(1-x^k))^k))

Crossrefs

Cf. A038507, A343573.

Sequence in context: A363208 A088095 A333392 * A358279 A217576 A173280

Adjacent sequences: A358386 A358387 A358388 * A358390 A358391 A358392

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 13 2022

Status

approved