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a(n) = Sum_{d|n} binomial(d+n-1,n).
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%I #17 Apr 25 2021 02:22:30

%S 1,4,11,41,127,498,1717,6610,24366,93391,352717,1358826,5200301,

%T 20097076,77562773,300786339,1166803111,4539163784,17672631901,

%U 68933291834,269129233484,1052113994124,4116715363801,16124221819056,63205303242628,247961973949228,973469736360283

%N a(n) = Sum_{d|n} binomial(d+n-1,n).

%H Seiichi Manyama, <a href="/A343548/b343548.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = [x^n] Sum_{k>=1} x^k/(1 - x^k)^(n+1).

%F a(n) = [x^n] Sum_{k>=1} binomial(k+n-1,n) * x^k/(1 - x^k).

%t a[n_] := DivisorSum[n, Binomial[# + n - 1, n] &]; Array[a, 30] (* _Amiram Eldar_, Apr 25 2021 *)

%o (PARI) a(n) = sumdiv(n, d, binomial(d+n-1, n));

%Y Cf. A000005, A000203, A007437, A059358, A073570, A101289, A332508, A343549.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Apr 19 2021