A363668 - OEIS

%I #12 Jul 12 2023 01:01:56

%S 1,7,19,91,151,1135,1765,12355,28846,157917,352837,2280955,5200469,

%T 29986201,80469589,427061795,1166803399,6211188028,17672632261,

%U 89483074521,271071666724,1316291647997,4116715364329,19595444140771,63205674328876,292318539358879

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

%F a(n) = [x^n] Sum_{k>0} (1/(1 - k*x^k)^n - 1).

%t a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n - 1, #] &]; Array[a, 30] (* _Amiram Eldar_, Jul 12 2023 *)

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

%Y Cf. A055225, A362683, A363639, A363640.

%Y Cf. A343549, A363669.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 14 2023