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a(n) = sigma(2n,n) for n>0 with a(0)=1.
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%I #15 Jul 09 2022 11:10:21

%S 1,3,21,252,4369,103158,3037530,106237176,4311810305,198756808749,

%T 10250010815226,584603613083988,36529334450076658,2481455748310337022,

%U 182070232515259616850,14349345894391097803752

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

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

%H Michel Marcus, <a href="/A179504/b179504.txt">Table of n, a(n) for n = 0..100</a>

%F After initial term, equals the logarithmic derivative of A156360.

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

%F a(n) ~ (2*n)^n. - _Vaclav Kotesovec_, Aug 21 2017

%t Table[If[n == 0, 1, DivisorSigma[n, 2 n]], {n, 0, 15}] (* _Michael De Vlieger_, Jul 12 2017 *)

%o (PARI) a(n)=if(n==0,1,sigma(2*n,n))

%o (Python)

%o from sympy import divisor_sigma

%o def A179504(n): return divisor_sigma(n<<1,n) if n else 1 # _Chai Wah Wu_, Jul 08 2022

%K nonn

%O 0,2

%A _Paul D. Hanna_, Sep 21 2010