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 A332508 a(n) = Sum_{d|n} binomial(n+d-2, n-1). 7

%I

%S 1,3,7,25,71,280,925,3561,12916,49346,184757,710255,2704157,10427747,

%T 40119781,155288897,601080391,2334714319,9075135301,35352181116,

%U 137846759282,538302226628,2104098963721,8233718962365,32247603703576,126412458920775,495918551104687

%N a(n) = Sum_{d|n} binomial(n+d-2, n-1).

%H Seiichi Manyama, <a href="/A332508/b332508.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.

%t Table[DivisorSum[n, Binomial[n + # - 2, n - 1] &], {n, 1, 27}]

%t Table[SeriesCoefficient[Sum[x^k/(1 - x^k)^n, {k, 1, n}], {x, 0, n}], {n, 1, 27}]

%o (PARI) a(n) = sumdiv(n, d, binomial(n+d-2, n-1)); \\ _Michel Marcus_, Feb 14 2020

%Y Cf. A000005, A000203, A007437, A059358, A073570, A101289, A308814, A332470.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Feb 14 2020

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Last modified July 28 17:15 EDT 2021. Contains 346335 sequences. (Running on oeis4.)