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
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..1655
Programs
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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
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Mathematica
a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n, n] &]; Array[a, 30] (* Amiram Eldar, Jul 05 2023 *)
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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).
Comments