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%I #18 Nov 23 2023 20:21:11
%S 2,12,32,150,282,1890,3488,21582,54650,282612,705564,4072224,10400782,
%T 55006530,158987232,790611350,2333606526,11573213196,35345264180,
%U 168673694070,540848064614,2500462200182,8233430728152,37445946291600,126411051769652
%N a(n) = Sum_{d|n} (n/d)^d * binomial(d+n,n).
%C All terms are even. - _Robert Israel_, Nov 23 2023
%H Robert Israel, <a href="/A363661/b363661.txt">Table of n, a(n) for n = 1..1655</a>
%F a(n) = [x^n] Sum_{k>0} (1/(1 - k*x^k)^(n+1) - 1).
%p f:= proc(n) local d;
%p add((n/d)^d * binomial(n+d,n), d = numtheory:-divisors(n))
%p end proc:
%p map(f, [$1..30]); # _Robert Israel_, Nov 23 2023
%t a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n, n] &]; Array[a, 30] (* _Amiram Eldar_, Jul 05 2023 *)
%o (PARI) a(n) = sumdiv(n, d, (n/d)^d*binomial(d+n, n));
%Y Cf. A362683, A363639, A363640.
%Y Cf. A055225, A363660, A363662, A363663.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Jun 14 2023
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