A179504 a(n) = sigma(2n,n) for n>0 with a(0)=1.

1, 3, 21, 252, 4369, 103158, 3037530, 106237176, 4311810305, 198756808749, 10250010815226, 584603613083988, 36529334450076658, 2481455748310337022, 182070232515259616850, 14349345894391097803752

Offset

0,2

Comments

sigma(n,k) denotes the sum of the k-th powers of the divisors of n.

Links

Michel Marcus, Table of n, a(n) for n = 0..100

Formula

After initial term, equals the logarithmic derivative of A156360.

Conjecture: a(n) = A023887(n)*((2^n - 1)/(2^(n*(A007814(n) + 1)) - 1) + 2^n) for n > 0. - Velin Yanev, Jul 08 2017

a(n) ~ (2*n)^n. - Vaclav Kotesovec, Aug 21 2017

Mathematica

Table[If[n == 0, 1, DivisorSigma[n, 2 n]], {n, 0, 15}] (* Michael De Vlieger, Jul 12 2017 *)

Prog

(PARI) a(n)=if(n==0, 1, sigma(2*n, n))
(Python)
from sympy import divisor_sigma
def A179504(n): return divisor_sigma(n<<1, n) if n else 1 # Chai Wah Wu, Jul 08 2022

Crossrefs

Sequence in context: A205319 A355099 A209917 * A197716 A336638 A317059

Adjacent sequences: A179501 A179502 A179503 * A179505 A179506 A179507

Keyword

nonn

Author

Paul D. Hanna, Sep 21 2010

Status

approved