A363661 a(n) = Sum_{d|n} (n/d)^d * binomial(d+n,n).

2, 12, 32, 150, 282, 1890, 3488, 21582, 54650, 282612, 705564, 4072224, 10400782, 55006530, 158987232, 790611350, 2333606526, 11573213196, 35345264180, 168673694070, 540848064614, 2500462200182, 8233430728152, 37445946291600, 126411051769652

Offset: 1

Author

Seiichi Manyama, Jun 14 2023

Keywords

• nonn

Comments

All terms are even. - Robert Israel, Nov 23 2023

Links

• Robert Israel, Table of n, a(n) for n = 1..1655

Crossrefs

Cf. A362683, A363639, A363640.

Cf. A055225, A363660, A363662, A363663.

Programs

Maple

f:= proc(n) local d;
   add((n/d)^d * binomial(n+d,n), d = numtheory:-divisors(n))
end proc:
map(f, [$1..30]); # Robert Israel, Nov 23 2023

Mathematica

a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n, n] &]; Array[a, 30] (* Amiram Eldar, Jul 05 2023 *)

PARI

a(n) = sumdiv(n, d, (n/d)^d*binomial(d+n, n));

Formula

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