A363669 - OEIS

%I #11 Jul 12 2023 01:01:53

%S 1,11,91,1219,15751,299291,5766517,136667939,3490056406,100539251801,

%T 3138428729437,107169878769043,3937376390899589,155639310270607349,

%U 6568429274592664981,295186202455912472867,14063084452068891794119,708261127356256620907496

%N a(n) = Sum_{d|n} (n/d)^n * 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/#)^n * Binomial[# + n - 1, #] &]; Array[a, 20] (* _Amiram Eldar_, Jul 12 2023 *)

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

%Y Cf. A363646, A363647, A363648.

%Y Cf. A343549, A363668.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 14 2023